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

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


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

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

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

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

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

Solving
-20 + 1x + x2 = 36

Solving for variable 'x'.

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

Combine like terms: -20 + -36 = -56
-56 + 1x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-56 + 1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-8, 7}

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