6x+1=(1-3x)(6x+1)

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Solution for 6x+1=(1-3x)(6x+1) equation: 


Simplifying
6x + 1 = (1 + -3x)(6x + 1)

Reorder the terms:
1 + 6x = (1 + -3x)(6x + 1)

Reorder the terms:
1 + 6x = (1 + -3x)(1 + 6x)

Multiply (1 + -3x) * (1 + 6x)
1 + 6x = (1(1 + 6x) + -3x * (1 + 6x))
1 + 6x = ((1 * 1 + 6x * 1) + -3x * (1 + 6x))
1 + 6x = ((1 + 6x) + -3x * (1 + 6x))
1 + 6x = (1 + 6x + (1 * -3x + 6x * -3x))
1 + 6x = (1 + 6x + (-3x + -18x2))

Combine like terms: 6x + -3x = 3x
1 + 6x = (1 + 3x + -18x2)

Add '-1' to each side of the equation.
1 + -1 + 6x = 1 + 3x + -1 + -18x2

Combine like terms: 1 + -1 = 0
0 + 6x = 1 + 3x + -1 + -18x2
6x = 1 + 3x + -1 + -18x2

Reorder the terms:
6x = 1 + -1 + 3x + -18x2

Combine like terms: 1 + -1 = 0
6x = 0 + 3x + -18x2
6x = 3x + -18x2

Solving
6x = 3x + -18x2

Solving for variable 'x'.

Combine like terms: 6x + -3x = 3x
3x + 18x2 = 3x + -18x2 + -3x + 18x2

Reorder the terms:
3x + 18x2 = 3x + -3x + -18x2 + 18x2

Combine like terms: 3x + -3x = 0
3x + 18x2 = 0 + -18x2 + 18x2
3x + 18x2 = -18x2 + 18x2

Combine like terms: -18x2 + 18x2 = 0
3x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 6x) = 0

Ignore the factor 3.

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 + 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
Solution
x = {0, -0.1666666667}

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