12(x-9)(2x+7)=0

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Solution for 12(x-9)(2x+7)=0 equation: 


Simplifying
12(x + -9)(2x + 7) = 0

Reorder the terms:
12(-9 + x)(2x + 7) = 0

Reorder the terms:
12(-9 + x)(7 + 2x) = 0

Multiply (-9 + x) * (7 + 2x)
12(-9(7 + 2x) + x(7 + 2x)) = 0
12((7 * -9 + 2x * -9) + x(7 + 2x)) = 0
12((-63 + -18x) + x(7 + 2x)) = 0
12(-63 + -18x + (7 * x + 2x * x)) = 0
12(-63 + -18x + (7x + 2x2)) = 0

Combine like terms: -18x + 7x = -11x
12(-63 + -11x + 2x2) = 0
(-63 * 12 + -11x * 12 + 2x2 * 12) = 0
(-756 + -132x + 24x2) = 0

Solving
-756 + -132x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-63 + -11x + 2x2) = 0

Factor a trinomial.
12((-7 + -2x)(9 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 9}

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