(x-4)(x+5)=-3(x-4)

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Solution for (x-4)(x+5)=-3(x-4) equation: 


Simplifying
(x + -4)(x + 5) = -3(x + -4)

Reorder the terms:
(-4 + x)(x + 5) = -3(x + -4)

Reorder the terms:
(-4 + x)(5 + x) = -3(x + -4)

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = -3(x + -4)
((5 * -4 + x * -4) + x(5 + x)) = -3(x + -4)
((-20 + -4x) + x(5 + x)) = -3(x + -4)
(-20 + -4x + (5 * x + x * x)) = -3(x + -4)
(-20 + -4x + (5x + x2)) = -3(x + -4)

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = -3(x + -4)

Reorder the terms:
-20 + 1x + x2 = -3(-4 + x)
-20 + 1x + x2 = (-4 * -3 + x * -3)
-20 + 1x + x2 = (12 + -3x)

Solving
-20 + 1x + x2 = 12 + -3x

Solving for variable 'x'.

Reorder the terms:
-20 + -12 + 1x + 3x + x2 = 12 + -3x + -12 + 3x

Combine like terms: -20 + -12 = -32
-32 + 1x + 3x + x2 = 12 + -3x + -12 + 3x

Combine like terms: 1x + 3x = 4x
-32 + 4x + x2 = 12 + -3x + -12 + 3x

Reorder the terms:
-32 + 4x + x2 = 12 + -12 + -3x + 3x

Combine like terms: 12 + -12 = 0
-32 + 4x + x2 = 0 + -3x + 3x
-32 + 4x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-32 + 4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}

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