(x-6)(x+9)=-4(x+9)

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Solution for (x-6)(x+9)=-4(x+9) equation: 


Simplifying
(x + -6)(x + 9) = -4(x + 9)

Reorder the terms:
(-6 + x)(x + 9) = -4(x + 9)

Reorder the terms:
(-6 + x)(9 + x) = -4(x + 9)

Multiply (-6 + x) * (9 + x)
(-6(9 + x) + x(9 + x)) = -4(x + 9)
((9 * -6 + x * -6) + x(9 + x)) = -4(x + 9)
((-54 + -6x) + x(9 + x)) = -4(x + 9)
(-54 + -6x + (9 * x + x * x)) = -4(x + 9)
(-54 + -6x + (9x + x2)) = -4(x + 9)

Combine like terms: -6x + 9x = 3x
(-54 + 3x + x2) = -4(x + 9)

Reorder the terms:
-54 + 3x + x2 = -4(9 + x)
-54 + 3x + x2 = (9 * -4 + x * -4)
-54 + 3x + x2 = (-36 + -4x)

Solving
-54 + 3x + x2 = -36 + -4x

Solving for variable 'x'.

Reorder the terms:
-54 + 36 + 3x + 4x + x2 = -36 + -4x + 36 + 4x

Combine like terms: -54 + 36 = -18
-18 + 3x + 4x + x2 = -36 + -4x + 36 + 4x

Combine like terms: 3x + 4x = 7x
-18 + 7x + x2 = -36 + -4x + 36 + 4x

Reorder the terms:
-18 + 7x + x2 = -36 + 36 + -4x + 4x

Combine like terms: -36 + 36 = 0
-18 + 7x + x2 = 0 + -4x + 4x
-18 + 7x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-18 + 7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -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 '(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 = {-9, 2}

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