(x-9)(x+7)=-7(x+7)

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Solution for (x-9)(x+7)=-7(x+7) equation: 


Simplifying
(x + -9)(x + 7) = -7(x + 7)

Reorder the terms:
(-9 + x)(x + 7) = -7(x + 7)

Reorder the terms:
(-9 + x)(7 + x) = -7(x + 7)

Multiply (-9 + x) * (7 + x)
(-9(7 + x) + x(7 + x)) = -7(x + 7)
((7 * -9 + x * -9) + x(7 + x)) = -7(x + 7)
((-63 + -9x) + x(7 + x)) = -7(x + 7)
(-63 + -9x + (7 * x + x * x)) = -7(x + 7)
(-63 + -9x + (7x + x2)) = -7(x + 7)

Combine like terms: -9x + 7x = -2x
(-63 + -2x + x2) = -7(x + 7)

Reorder the terms:
-63 + -2x + x2 = -7(7 + x)
-63 + -2x + x2 = (7 * -7 + x * -7)
-63 + -2x + x2 = (-49 + -7x)

Solving
-63 + -2x + x2 = -49 + -7x

Solving for variable 'x'.

Reorder the terms:
-63 + 49 + -2x + 7x + x2 = -49 + -7x + 49 + 7x

Combine like terms: -63 + 49 = -14
-14 + -2x + 7x + x2 = -49 + -7x + 49 + 7x

Combine like terms: -2x + 7x = 5x
-14 + 5x + x2 = -49 + -7x + 49 + 7x

Reorder the terms:
-14 + 5x + x2 = -49 + 49 + -7x + 7x

Combine like terms: -49 + 49 = 0
-14 + 5x + x2 = 0 + -7x + 7x
-14 + 5x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-14 + 5x + x2 = 0

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


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7, 2}

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