(14x+7)(8x-12)=0

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Solution for (14x+7)(8x-12)=0 equation:


Simplifying
(14x + 7)(8x + -12) = 0

Reorder the terms:
(7 + 14x)(8x + -12) = 0

Reorder the terms:
(7 + 14x)(-12 + 8x) = 0

Multiply (7 + 14x) * (-12 + 8x)
(7(-12 + 8x) + 14x * (-12 + 8x)) = 0
((-12 * 7 + 8x * 7) + 14x * (-12 + 8x)) = 0
((-84 + 56x) + 14x * (-12 + 8x)) = 0
(-84 + 56x + (-12 * 14x + 8x * 14x)) = 0
(-84 + 56x + (-168x + 112x2)) = 0

Combine like terms: 56x + -168x = -112x
(-84 + -112x + 112x2) = 0

Solving
-84 + -112x + 112x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '28'.
28(-3 + -4x + 4x2) = 0

Factor a trinomial.
28((-1 + -2x)(3 + -2x)) = 0

Ignore the factor 28.

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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.5, 1.5}

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