(2x+9)(x-6)=-2(6-x)

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Solution for (2x+9)(x-6)=-2(6-x) equation: 


Simplifying
(2x + 9)(x + -6) = -2(6 + -1x)

Reorder the terms:
(9 + 2x)(x + -6) = -2(6 + -1x)

Reorder the terms:
(9 + 2x)(-6 + x) = -2(6 + -1x)

Multiply (9 + 2x) * (-6 + x)
(9(-6 + x) + 2x * (-6 + x)) = -2(6 + -1x)
((-6 * 9 + x * 9) + 2x * (-6 + x)) = -2(6 + -1x)
((-54 + 9x) + 2x * (-6 + x)) = -2(6 + -1x)
(-54 + 9x + (-6 * 2x + x * 2x)) = -2(6 + -1x)
(-54 + 9x + (-12x + 2x2)) = -2(6 + -1x)

Combine like terms: 9x + -12x = -3x
(-54 + -3x + 2x2) = -2(6 + -1x)
-54 + -3x + 2x2 = (6 * -2 + -1x * -2)
-54 + -3x + 2x2 = (-12 + 2x)

Solving
-54 + -3x + 2x2 = -12 + 2x

Solving for variable 'x'.

Reorder the terms:
-54 + 12 + -3x + -2x + 2x2 = -12 + 2x + 12 + -2x

Combine like terms: -54 + 12 = -42
-42 + -3x + -2x + 2x2 = -12 + 2x + 12 + -2x

Combine like terms: -3x + -2x = -5x
-42 + -5x + 2x2 = -12 + 2x + 12 + -2x

Reorder the terms:
-42 + -5x + 2x2 = -12 + 12 + 2x + -2x

Combine like terms: -12 + 12 = 0
-42 + -5x + 2x2 = 0 + 2x + -2x
-42 + -5x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-42 + -5x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(6 + -1x) = 0


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

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3.5, 6}

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