(8x-7)(9x+6)=0

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Solution for (8x-7)(9x+6)=0 equation: 


Simplifying
(8x + -7)(9x + 6) = 0

Reorder the terms:
(-7 + 8x)(9x + 6) = 0

Reorder the terms:
(-7 + 8x)(6 + 9x) = 0

Multiply (-7 + 8x) * (6 + 9x)
(-7(6 + 9x) + 8x * (6 + 9x)) = 0
((6 * -7 + 9x * -7) + 8x * (6 + 9x)) = 0
((-42 + -63x) + 8x * (6 + 9x)) = 0
(-42 + -63x + (6 * 8x + 9x * 8x)) = 0
(-42 + -63x + (48x + 72x2)) = 0

Combine like terms: -63x + 48x = -15x
(-42 + -15x + 72x2) = 0

Solving
-42 + -15x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -5x + 24x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 0.875}

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