(3x+8)(4x-2)=0

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Solution for (3x+8)(4x-2)=0 equation: 


Simplifying
(3x + 8)(4x + -2) = 0

Reorder the terms:
(8 + 3x)(4x + -2) = 0

Reorder the terms:
(8 + 3x)(-2 + 4x) = 0

Multiply (8 + 3x) * (-2 + 4x)
(8(-2 + 4x) + 3x * (-2 + 4x)) = 0
((-2 * 8 + 4x * 8) + 3x * (-2 + 4x)) = 0
((-16 + 32x) + 3x * (-2 + 4x)) = 0
(-16 + 32x + (-2 * 3x + 4x * 3x)) = 0
(-16 + 32x + (-6x + 12x2)) = 0

Combine like terms: 32x + -6x = 26x
(-16 + 26x + 12x2) = 0

Solving
-16 + 26x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 13x + 6x2) = 0

Factor a trinomial.
2((-8 + -3x)(1 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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 = {-2.666666667, 0.5}

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