12(x-7)(2x+1)=0

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Solution for 12(x-7)(2x+1)=0 equation: 


Simplifying
12(x + -7)(2x + 1) = 0

Reorder the terms:
12(-7 + x)(2x + 1) = 0

Reorder the terms:
12(-7 + x)(1 + 2x) = 0

Multiply (-7 + x) * (1 + 2x)
12(-7(1 + 2x) + x(1 + 2x)) = 0
12((1 * -7 + 2x * -7) + x(1 + 2x)) = 0
12((-7 + -14x) + x(1 + 2x)) = 0
12(-7 + -14x + (1 * x + 2x * x)) = 0
12(-7 + -14x + (1x + 2x2)) = 0

Combine like terms: -14x + 1x = -13x
12(-7 + -13x + 2x2) = 0
(-7 * 12 + -13x * 12 + 2x2 * 12) = 0
(-84 + -156x + 24x2) = 0

Solving
-84 + -156x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + -13x + 2x2) = 0

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

Ignore the factor 12.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
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
Solution
x = {-0.5, 7}

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