(8x-2)x(3x+1)=0

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Solution for (8x-2)x(3x+1)=0 equation: 


Simplifying
(8x + -2) * x(3x + 1) = 0

Reorder the terms:
(-2 + 8x) * x(3x + 1) = 0

Reorder the terms:
(-2 + 8x) * x(1 + 3x) = 0

Reorder the terms for easier multiplication:
x(-2 + 8x)(1 + 3x) = 0

Multiply (-2 + 8x) * (1 + 3x)
x(-2(1 + 3x) + 8x * (1 + 3x)) = 0
x((1 * -2 + 3x * -2) + 8x * (1 + 3x)) = 0
x((-2 + -6x) + 8x * (1 + 3x)) = 0
x(-2 + -6x + (1 * 8x + 3x * 8x)) = 0
x(-2 + -6x + (8x + 24x2)) = 0

Combine like terms: -6x + 8x = 2x
x(-2 + 2x + 24x2) = 0
(-2 * x + 2x * x + 24x2 * x) = 0
(-2x + 2x2 + 24x3) = 0

Solving
-2x + 2x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + x + 12x2) = 0

Factor a trinomial.
2x((-1 + -3x)(1 + -4x)) = 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 '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, -0.3333333333, 0.25}

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