(x-4)(x+3)=-2x

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Solution for (x-4)(x+3)=-2x equation: 


Simplifying
(x + -4)(x + 3) = -2x

Reorder the terms:
(-4 + x)(x + 3) = -2x

Reorder the terms:
(-4 + x)(3 + x) = -2x

Multiply (-4 + x) * (3 + x)
(-4(3 + x) + x(3 + x)) = -2x
((3 * -4 + x * -4) + x(3 + x)) = -2x
((-12 + -4x) + x(3 + x)) = -2x
(-12 + -4x + (3 * x + x * x)) = -2x
(-12 + -4x + (3x + x2)) = -2x

Combine like terms: -4x + 3x = -1x
(-12 + -1x + x2) = -2x

Solving
-12 + -1x + x2 = -2x

Solving for variable 'x'.

Reorder the terms:
-12 + -1x + 2x + x2 = -2x + 2x

Combine like terms: -1x + 2x = 1x
-12 + 1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}

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