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

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


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

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

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

Multiply (-6 + 8x) * (8 + 9x)
(-6(8 + 9x) + 8x * (8 + 9x)) = 0
((8 * -6 + 9x * -6) + 8x * (8 + 9x)) = 0
((-48 + -54x) + 8x * (8 + 9x)) = 0
(-48 + -54x + (8 * 8x + 9x * 8x)) = 0
(-48 + -54x + (64x + 72x2)) = 0

Combine like terms: -54x + 64x = 10x
(-48 + 10x + 72x2) = 0

Solving
-48 + 10x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 5x + 36x2) = 0

Factor a trinomial.
2((-8 + -9x)(3 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -9x)' equal to zero and attempt to solve:

Simplifying
-8 + -9x = 0

Solving
-8 + -9x = 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 + -9x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9x = 0 + 8
-9x = 0 + 8

Combine like terms: 0 + 8 = 8
-9x = 8

Divide each side by '-9'.
x = -0.8888888889

Simplifying
x = -0.8888888889

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 = {-0.8888888889, 0.75}

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