(3x+4)(2x-2)=0

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Solution for (3x+4)(2x-2)=0 equation: 


Simplifying
(3x + 4)(2x + -2) = 0

Reorder the terms:
(4 + 3x)(2x + -2) = 0

Reorder the terms:
(4 + 3x)(-2 + 2x) = 0

Multiply (4 + 3x) * (-2 + 2x)
(4(-2 + 2x) + 3x * (-2 + 2x)) = 0
((-2 * 4 + 2x * 4) + 3x * (-2 + 2x)) = 0
((-8 + 8x) + 3x * (-2 + 2x)) = 0
(-8 + 8x + (-2 * 3x + 2x * 3x)) = 0
(-8 + 8x + (-6x + 6x2)) = 0

Combine like terms: 8x + -6x = 2x
(-8 + 2x + 6x2) = 0

Solving
-8 + 2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + x + 3x2) = 0

Factor a trinomial.
2((-4 + -3x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.333333333, 1}

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