(6x+2)(8x-1)=0

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Solution for (6x+2)(8x-1)=0 equation: 


Simplifying
(6x + 2)(8x + -1) = 0

Reorder the terms:
(2 + 6x)(8x + -1) = 0

Reorder the terms:
(2 + 6x)(-1 + 8x) = 0

Multiply (2 + 6x) * (-1 + 8x)
(2(-1 + 8x) + 6x * (-1 + 8x)) = 0
((-1 * 2 + 8x * 2) + 6x * (-1 + 8x)) = 0
((-2 + 16x) + 6x * (-1 + 8x)) = 0
(-2 + 16x + (-1 * 6x + 8x * 6x)) = 0
(-2 + 16x + (-6x + 48x2)) = 0

Combine like terms: 16x + -6x = 10x
(-2 + 10x + 48x2) = 0

Solving
-2 + 10x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 5x + 24x2) = 0

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

Ignore the factor 2.

Subproblem 1
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 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve:

Simplifying
1 + -8x = 0

Solving
1 + -8x = 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 + -8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x = 0 + -1
-8x = 0 + -1

Combine like terms: 0 + -1 = -1
-8x = -1

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125
Solution
x = {-0.3333333333, 0.125}

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