(3x+4)(4x-2)=-8

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Solution for (3x+4)(4x-2)=-8 equation: 


Simplifying
(3x + 4)(4x + -2) = -8

Reorder the terms:
(4 + 3x)(4x + -2) = -8

Reorder the terms:
(4 + 3x)(-2 + 4x) = -8

Multiply (4 + 3x) * (-2 + 4x)
(4(-2 + 4x) + 3x * (-2 + 4x)) = -8
((-2 * 4 + 4x * 4) + 3x * (-2 + 4x)) = -8
((-8 + 16x) + 3x * (-2 + 4x)) = -8
(-8 + 16x + (-2 * 3x + 4x * 3x)) = -8
(-8 + 16x + (-6x + 12x2)) = -8

Combine like terms: 16x + -6x = 10x
(-8 + 10x + 12x2) = -8

Add '8' to each side of the equation.
-8 + 10x + 8 + 12x2 = -8 + 8

Reorder the terms:
-8 + 8 + 10x + 12x2 = -8 + 8

Combine like terms: -8 + 8 = 0
0 + 10x + 12x2 = -8 + 8
10x + 12x2 = -8 + 8

Combine like terms: -8 + 8 = 0
10x + 12x2 = 0

Solving
10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + 6x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0, -0.8333333333}

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