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

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


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

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

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

Multiply (8 + 6x) * (-6 + 8x)
(8(-6 + 8x) + 6x * (-6 + 8x)) = 0
((-6 * 8 + 8x * 8) + 6x * (-6 + 8x)) = 0
((-48 + 64x) + 6x * (-6 + 8x)) = 0
(-48 + 64x + (-6 * 6x + 8x * 6x)) = 0
(-48 + 64x + (-36x + 48x2)) = 0

Combine like terms: 64x + -36x = 28x
(-48 + 28x + 48x2) = 0

Solving
-48 + 28x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 7x + 12x2) = 0

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

Ignore the factor 4.

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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.333333333, 0.75}

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