(6x-8)(4x+4)=0

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Solution for (6x-8)(4x+4)=0 equation: 


Simplifying
(6x + -8)(4x + 4) = 0

Reorder the terms:
(-8 + 6x)(4x + 4) = 0

Reorder the terms:
(-8 + 6x)(4 + 4x) = 0

Multiply (-8 + 6x) * (4 + 4x)
(-8(4 + 4x) + 6x * (4 + 4x)) = 0
((4 * -8 + 4x * -8) + 6x * (4 + 4x)) = 0
((-32 + -32x) + 6x * (4 + 4x)) = 0
(-32 + -32x + (4 * 6x + 4x * 6x)) = 0
(-32 + -32x + (24x + 24x2)) = 0

Combine like terms: -32x + 24x = -8x
(-32 + -8x + 24x2) = 0

Solving
-32 + -8x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -1x + 3x2) = 0

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

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 1.333333333}

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