(3x-1)(2x+1)=(6x+3)(3x-1)

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Solution for (3x-1)(2x+1)=(6x+3)(3x-1) equation: 


Simplifying
(3x + -1)(2x + 1) = (6x + 3)(3x + -1)

Reorder the terms:
(-1 + 3x)(2x + 1) = (6x + 3)(3x + -1)

Reorder the terms:
(-1 + 3x)(1 + 2x) = (6x + 3)(3x + -1)

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

Combine like terms: -2x + 3x = 1x
(-1 + 1x + 6x2) = (6x + 3)(3x + -1)

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

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

Multiply (3 + 6x) * (-1 + 3x)
-1 + 1x + 6x2 = (3(-1 + 3x) + 6x * (-1 + 3x))
-1 + 1x + 6x2 = ((-1 * 3 + 3x * 3) + 6x * (-1 + 3x))
-1 + 1x + 6x2 = ((-3 + 9x) + 6x * (-1 + 3x))
-1 + 1x + 6x2 = (-3 + 9x + (-1 * 6x + 3x * 6x))
-1 + 1x + 6x2 = (-3 + 9x + (-6x + 18x2))

Combine like terms: 9x + -6x = 3x
-1 + 1x + 6x2 = (-3 + 3x + 18x2)

Solving
-1 + 1x + 6x2 = -3 + 3x + 18x2

Solving for variable 'x'.

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

Combine like terms: -1 + 3 = 2
2 + 1x + -3x + 6x2 + -18x2 = -3 + 3x + 18x2 + 3 + -3x + -18x2

Combine like terms: 1x + -3x = -2x
2 + -2x + 6x2 + -18x2 = -3 + 3x + 18x2 + 3 + -3x + -18x2

Combine like terms: 6x2 + -18x2 = -12x2
2 + -2x + -12x2 = -3 + 3x + 18x2 + 3 + -3x + -18x2

Reorder the terms:
2 + -2x + -12x2 = -3 + 3 + 3x + -3x + 18x2 + -18x2

Combine like terms: -3 + 3 = 0
2 + -2x + -12x2 = 0 + 3x + -3x + 18x2 + -18x2
2 + -2x + -12x2 = 3x + -3x + 18x2 + -18x2

Combine like terms: 3x + -3x = 0
2 + -2x + -12x2 = 0 + 18x2 + -18x2
2 + -2x + -12x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
2 + -2x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -1x + -6x2) = 0

Factor a trinomial.
2((1 + -3x)(1 + 2x)) = 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 + 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 = {0.3333333333, -0.5}

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