(x-9)(x+2)=-3(x-9)

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Solution for (x-9)(x+2)=-3(x-9) equation: 


Simplifying
(x + -9)(x + 2) = -3(x + -9)

Reorder the terms:
(-9 + x)(x + 2) = -3(x + -9)

Reorder the terms:
(-9 + x)(2 + x) = -3(x + -9)

Multiply (-9 + x) * (2 + x)
(-9(2 + x) + x(2 + x)) = -3(x + -9)
((2 * -9 + x * -9) + x(2 + x)) = -3(x + -9)
((-18 + -9x) + x(2 + x)) = -3(x + -9)
(-18 + -9x + (2 * x + x * x)) = -3(x + -9)
(-18 + -9x + (2x + x2)) = -3(x + -9)

Combine like terms: -9x + 2x = -7x
(-18 + -7x + x2) = -3(x + -9)

Reorder the terms:
-18 + -7x + x2 = -3(-9 + x)
-18 + -7x + x2 = (-9 * -3 + x * -3)
-18 + -7x + x2 = (27 + -3x)

Solving
-18 + -7x + x2 = 27 + -3x

Solving for variable 'x'.

Reorder the terms:
-18 + -27 + -7x + 3x + x2 = 27 + -3x + -27 + 3x

Combine like terms: -18 + -27 = -45
-45 + -7x + 3x + x2 = 27 + -3x + -27 + 3x

Combine like terms: -7x + 3x = -4x
-45 + -4x + x2 = 27 + -3x + -27 + 3x

Reorder the terms:
-45 + -4x + x2 = 27 + -27 + -3x + 3x

Combine like terms: 27 + -27 = 0
-45 + -4x + x2 = 0 + -3x + 3x
-45 + -4x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -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 '(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 = {-5, 9}

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