(x-7)(x+9)=-3(x+9)

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Solution for (x-7)(x+9)=-3(x+9) equation: 


Simplifying
(x + -7)(x + 9) = -3(x + 9)

Reorder the terms:
(-7 + x)(x + 9) = -3(x + 9)

Reorder the terms:
(-7 + x)(9 + x) = -3(x + 9)

Multiply (-7 + x) * (9 + x)
(-7(9 + x) + x(9 + x)) = -3(x + 9)
((9 * -7 + x * -7) + x(9 + x)) = -3(x + 9)
((-63 + -7x) + x(9 + x)) = -3(x + 9)
(-63 + -7x + (9 * x + x * x)) = -3(x + 9)
(-63 + -7x + (9x + x2)) = -3(x + 9)

Combine like terms: -7x + 9x = 2x
(-63 + 2x + x2) = -3(x + 9)

Reorder the terms:
-63 + 2x + x2 = -3(9 + x)
-63 + 2x + x2 = (9 * -3 + x * -3)
-63 + 2x + x2 = (-27 + -3x)

Solving
-63 + 2x + x2 = -27 + -3x

Solving for variable 'x'.

Reorder the terms:
-63 + 27 + 2x + 3x + x2 = -27 + -3x + 27 + 3x

Combine like terms: -63 + 27 = -36
-36 + 2x + 3x + x2 = -27 + -3x + 27 + 3x

Combine like terms: 2x + 3x = 5x
-36 + 5x + x2 = -27 + -3x + 27 + 3x

Reorder the terms:
-36 + 5x + x2 = -27 + 27 + -3x + 3x

Combine like terms: -27 + 27 = 0
-36 + 5x + x2 = 0 + -3x + 3x
-36 + 5x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-9, 4}

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