(3x+1)(2x-2)=64

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Solution for (3x+1)(2x-2)=64 equation: 


Simplifying
(3x + 1)(2x + -2) = 64

Reorder the terms:
(1 + 3x)(2x + -2) = 64

Reorder the terms:
(1 + 3x)(-2 + 2x) = 64

Multiply (1 + 3x) * (-2 + 2x)
(1(-2 + 2x) + 3x * (-2 + 2x)) = 64
((-2 * 1 + 2x * 1) + 3x * (-2 + 2x)) = 64
((-2 + 2x) + 3x * (-2 + 2x)) = 64
(-2 + 2x + (-2 * 3x + 2x * 3x)) = 64
(-2 + 2x + (-6x + 6x2)) = 64

Combine like terms: 2x + -6x = -4x
(-2 + -4x + 6x2) = 64

Solving
-2 + -4x + 6x2 = 64

Solving for variable 'x'.

Reorder the terms:
-2 + -64 + -4x + 6x2 = 64 + -64

Combine like terms: -2 + -64 = -66
-66 + -4x + 6x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-66 + -4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -2x + 3x2) = 0

Factor a trinomial.
2((-3 + -1x)(11 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {-3, 3.666666667}

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