(7x-8)(6x+8)=0

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Solution for (7x-8)(6x+8)=0 equation: 


Simplifying
(7x + -8)(6x + 8) = 0

Reorder the terms:
(-8 + 7x)(6x + 8) = 0

Reorder the terms:
(-8 + 7x)(8 + 6x) = 0

Multiply (-8 + 7x) * (8 + 6x)
(-8(8 + 6x) + 7x * (8 + 6x)) = 0
((8 * -8 + 6x * -8) + 7x * (8 + 6x)) = 0
((-64 + -48x) + 7x * (8 + 6x)) = 0
(-64 + -48x + (8 * 7x + 6x * 7x)) = 0
(-64 + -48x + (56x + 42x2)) = 0

Combine like terms: -48x + 56x = 8x
(-64 + 8x + 42x2) = 0

Solving
-64 + 8x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4x + 21x2) = 0

Factor a trinomial.
2((-4 + -3x)(8 + -7x)) = 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 '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 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 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-1.333333333, 1.142857143}

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