Chris Cuts Half A Rectangular Lawn, 40m By 30m, By Mowing Strips Of Equal Width Around The Perimeter, Jonah Cuts The Small Rectangular Left. How Wide A Strip Does Chris Cut So That They Share The Work Equally?

The lawn is 40x30 = 1200 m².

When Chris gets finished cutting a strip x meters wide around the outside, the resulting rectangle will be (40-2x) by (30-2x). We want to find x so that this will be half of the lawn area.

1200/2 = (40-2x)(30-2x)
600 = 1200 - 60x - 80x + 4x²
0 = 4x² -140x + 600
x² - 35x + 150 = 0
(x - 5)(x - 30) = 0
x = 5 meters or x = 30 meters. (The latter choice is absurd, so we choose the former.)
Chris mowed strips around the outside totaling 5 m wide along each side of the lawn.

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You have not provided an equation, so there is nothing to solve.  Have you omitted some of the directions about what you are required to do (e.g., write it another form or factor it), or have you possibly left out some of the problem?  It might help if know what you are studying in your mathematics class.
 
OK, I see you have updated your question and you want to factor the the trinomial.  Oddman is correct, there are no nice factors.  Typically you like to get this form of a problem on the left side of an equation with 0 on the right side.  This is called a quadratic equation.  If it is easy to factor, you can use the factors to quickly solve for x.  If it is not easy to factor. As in he case, then you will usually apply the quadratic formula to find x.  Good luck.
Assume that the size of the rectangle that Jonah cuts is x meters long and y meters wide, and that the strip Chris cuts is z meters wide.
 
So, the length of the lawn is x + 2z, which we know is 40m.  The width of lawn is y + 2z, which we know is 30m.   We also want the area that Jonah cuts to be equal to the area that Chris cuts.  In other words we want the area that Jonah cuts to be equal to have the area of the lawn, which we know is (40m * 30m) / 2, or 600m².  We have three unknowns, and now we have enough information to write three equations.
 
x + 2z = 40m
y + 2z = 30m
x * y =  600m²
 
solve the first equation for x to get
x = 40m – 2z
 
solve the second equation for y to get
y = 30m – 2z
 
substitute the answers into the third equation and solve for z
(40m – 2z) * (30m – 2z) = 600m²
4z² - (60m * z) - (80m * z) + 1200 m² = 600m²
4z² - (140m * z) + 600m² = 0
z² - (35m * z) + 150m² = 0
(z - 5m) * (z - 30m) = 0
The possible answers are z = 5m or z = 30m.  We know that 30m is not valid because the width of the lawn is only 30m, so the answer is 5m.

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