-4x(x+6)-2(x-9)=-12

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Solution for -4x(x+6)-2(x-9)=-12 equation: 


Simplifying
-4x(x + 6) + -2(x + -9) = -12

Reorder the terms:
-4x(6 + x) + -2(x + -9) = -12
(6 * -4x + x * -4x) + -2(x + -9) = -12
(-24x + -4x2) + -2(x + -9) = -12

Reorder the terms:
-24x + -4x2 + -2(-9 + x) = -12
-24x + -4x2 + (-9 * -2 + x * -2) = -12
-24x + -4x2 + (18 + -2x) = -12

Reorder the terms:
18 + -24x + -2x + -4x2 = -12

Combine like terms: -24x + -2x = -26x
18 + -26x + -4x2 = -12

Solving
18 + -26x + -4x2 = -12

Solving for variable 'x'.

Reorder the terms:
18 + 12 + -26x + -4x2 = -12 + 12

Combine like terms: 18 + 12 = 30
30 + -26x + -4x2 = -12 + 12

Combine like terms: -12 + 12 = 0
30 + -26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -13x + -2x2) = 0

Factor a trinomial.
2((1 + -1x)(15 + 2x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + 2x)' equal to zero and attempt to solve:

Simplifying
15 + 2x = 0

Solving
15 + 2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2x = 0 + -15
2x = 0 + -15

Combine like terms: 0 + -15 = -15
2x = -15

Divide each side by '2'.
x = -7.5

Simplifying
x = -7.5
Solution
x = {1, -7.5}

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