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

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


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

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

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

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

Combine like terms: -64x + 42x = -22x
(-56 + -22x + 48x2) = 0

Solving
-56 + -22x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + -11x + 24x2) = 0

Factor a trinomial.
2((-7 + -8x)(4 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -8x)' equal to zero and attempt to solve:

Simplifying
-7 + -8x = 0

Solving
-7 + -8x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -8x = 0 + 7

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

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

Divide each side by '-8'.
x = -0.875

Simplifying
x = -0.875

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 = {-0.875, 1.333333333}

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