(x-5)(x+4)=-2x

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Solution for (x-5)(x+4)=-2x equation: 


Simplifying
(x + -5)(x + 4) = -2x

Reorder the terms:
(-5 + x)(x + 4) = -2x

Reorder the terms:
(-5 + x)(4 + x) = -2x

Multiply (-5 + x) * (4 + x)
(-5(4 + x) + x(4 + x)) = -2x
((4 * -5 + x * -5) + x(4 + x)) = -2x
((-20 + -5x) + x(4 + x)) = -2x
(-20 + -5x + (4 * x + x * x)) = -2x
(-20 + -5x + (4x + x2)) = -2x

Combine like terms: -5x + 4x = -1x
(-20 + -1x + x2) = -2x

Solving
-20 + -1x + x2 = -2x

Solving for variable 'x'.

Reorder the terms:
-20 + -1x + 2x + x2 = -2x + 2x

Combine like terms: -1x + 2x = 1x
-20 + 1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-20 + 1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 4}

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