(3x-2)(2x+4)=56

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Solution for (3x-2)(2x+4)=56 equation: 


Simplifying
(3x + -2)(2x + 4) = 56

Reorder the terms:
(-2 + 3x)(2x + 4) = 56

Reorder the terms:
(-2 + 3x)(4 + 2x) = 56

Multiply (-2 + 3x) * (4 + 2x)
(-2(4 + 2x) + 3x * (4 + 2x)) = 56
((4 * -2 + 2x * -2) + 3x * (4 + 2x)) = 56
((-8 + -4x) + 3x * (4 + 2x)) = 56
(-8 + -4x + (4 * 3x + 2x * 3x)) = 56
(-8 + -4x + (12x + 6x2)) = 56

Combine like terms: -4x + 12x = 8x
(-8 + 8x + 6x2) = 56

Solving
-8 + 8x + 6x2 = 56

Solving for variable 'x'.

Reorder the terms:
-8 + -56 + 8x + 6x2 = 56 + -56

Combine like terms: -8 + -56 = -64
-64 + 8x + 6x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-64 + 8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4x + 3x2) = 0

Factor a trinomial.
2((-4 + -1x)(8 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-4, 2.666666667}

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