(x-4)(x-5)-(x+5)(x+4)=36

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Solution for (x-4)(x-5)-(x+5)(x+4)=36 equation: 


Simplifying
(x + -4)(x + -5) + -1(x + 5)(x + 4) = 36

Reorder the terms:
(-4 + x)(x + -5) + -1(x + 5)(x + 4) = 36

Reorder the terms:
(-4 + x)(-5 + x) + -1(x + 5)(x + 4) = 36

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x)) + -1(x + 5)(x + 4) = 36
((-5 * -4 + x * -4) + x(-5 + x)) + -1(x + 5)(x + 4) = 36
((20 + -4x) + x(-5 + x)) + -1(x + 5)(x + 4) = 36
(20 + -4x + (-5 * x + x * x)) + -1(x + 5)(x + 4) = 36
(20 + -4x + (-5x + x2)) + -1(x + 5)(x + 4) = 36

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2) + -1(x + 5)(x + 4) = 36

Reorder the terms:
20 + -9x + x2 + -1(5 + x)(x + 4) = 36

Reorder the terms:
20 + -9x + x2 + -1(5 + x)(4 + x) = 36

Multiply (5 + x) * (4 + x)
20 + -9x + x2 + -1(5(4 + x) + x(4 + x)) = 36
20 + -9x + x2 + -1((4 * 5 + x * 5) + x(4 + x)) = 36
20 + -9x + x2 + -1((20 + 5x) + x(4 + x)) = 36
20 + -9x + x2 + -1(20 + 5x + (4 * x + x * x)) = 36
20 + -9x + x2 + -1(20 + 5x + (4x + x2)) = 36

Combine like terms: 5x + 4x = 9x
20 + -9x + x2 + -1(20 + 9x + x2) = 36
20 + -9x + x2 + (20 * -1 + 9x * -1 + x2 * -1) = 36
20 + -9x + x2 + (-20 + -9x + -1x2) = 36

Reorder the terms:
20 + -20 + -9x + -9x + x2 + -1x2 = 36

Combine like terms: 20 + -20 = 0
0 + -9x + -9x + x2 + -1x2 = 36
-9x + -9x + x2 + -1x2 = 36

Combine like terms: -9x + -9x = -18x
-18x + x2 + -1x2 = 36

Combine like terms: x2 + -1x2 = 0
-18x + 0 = 36
-18x = 36

Solving
-18x = 36

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '-18'.
x = -2

Simplifying
x = -2

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