(4x-2)*6(2x+7)=0

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Solution for (4x-2)*6(2x+7)=0 equation: 


Simplifying
(4x + -2) * 6(2x + 7) = 0

Reorder the terms:
(-2 + 4x) * 6(2x + 7) = 0

Reorder the terms:
(-2 + 4x) * 6(7 + 2x) = 0

Reorder the terms for easier multiplication:
6(-2 + 4x)(7 + 2x) = 0

Multiply (-2 + 4x) * (7 + 2x)
6(-2(7 + 2x) + 4x * (7 + 2x)) = 0
6((7 * -2 + 2x * -2) + 4x * (7 + 2x)) = 0
6((-14 + -4x) + 4x * (7 + 2x)) = 0
6(-14 + -4x + (7 * 4x + 2x * 4x)) = 0
6(-14 + -4x + (28x + 8x2)) = 0

Combine like terms: -4x + 28x = 24x
6(-14 + 24x + 8x2) = 0
(-14 * 6 + 24x * 6 + 8x2 * 6) = 0
(-84 + 144x + 48x2) = 0

Solving
-84 + 144x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + 12x + 4x2) = 0

Factor a trinomial.
12((-7 + -2x)(1 + -2x)) = 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 '(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
Solution
x = {-3.5, 0.5}

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