(x-9)(2x+2)=-4(x-9)

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Solution for (x-9)(2x+2)=-4(x-9) equation:


Simplifying
(x + -9)(2x + 2) = -4(x + -9)

Reorder the terms:
(-9 + x)(2x + 2) = -4(x + -9)

Reorder the terms:
(-9 + x)(2 + 2x) = -4(x + -9)

Multiply (-9 + x) * (2 + 2x)
(-9(2 + 2x) + x(2 + 2x)) = -4(x + -9)
((2 * -9 + 2x * -9) + x(2 + 2x)) = -4(x + -9)
((-18 + -18x) + x(2 + 2x)) = -4(x + -9)
(-18 + -18x + (2 * x + 2x * x)) = -4(x + -9)
(-18 + -18x + (2x + 2x2)) = -4(x + -9)

Combine like terms: -18x + 2x = -16x
(-18 + -16x + 2x2) = -4(x + -9)

Reorder the terms:
-18 + -16x + 2x2 = -4(-9 + x)
-18 + -16x + 2x2 = (-9 * -4 + x * -4)
-18 + -16x + 2x2 = (36 + -4x)

Solving
-18 + -16x + 2x2 = 36 + -4x

Solving for variable 'x'.

Reorder the terms:
-18 + -36 + -16x + 4x + 2x2 = 36 + -4x + -36 + 4x

Combine like terms: -18 + -36 = -54
-54 + -16x + 4x + 2x2 = 36 + -4x + -36 + 4x

Combine like terms: -16x + 4x = -12x
-54 + -12x + 2x2 = 36 + -4x + -36 + 4x

Reorder the terms:
-54 + -12x + 2x2 = 36 + -36 + -4x + 4x

Combine like terms: 36 + -36 = 0
-54 + -12x + 2x2 = 0 + -4x + 4x
-54 + -12x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-54 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -6x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-3, 9}

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