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

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


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

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

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

Multiply 2 * 2
4x(1 + 3x) = 8x + 1
(1 * 4x + 3x * 4x) = 8x + 1
(4x + 12x2) = 8x + 1

Reorder the terms:
4x + 12x2 = 1 + 8x

Solving
4x + 12x2 = 1 + 8x

Solving for variable 'x'.

Reorder the terms:
-1 + 4x + -8x + 12x2 = 1 + 8x + -1 + -8x

Combine like terms: 4x + -8x = -4x
-1 + -4x + 12x2 = 1 + 8x + -1 + -8x

Reorder the terms:
-1 + -4x + 12x2 = 1 + -1 + 8x + -8x

Combine like terms: 1 + -1 = 0
-1 + -4x + 12x2 = 0 + 8x + -8x
-1 + -4x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-1 + -4x + 12x2 = 0

Factor a trinomial.
(-1 + -6x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

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 = {-0.1666666667, 0.5}

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