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

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


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

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

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

Multiply (-8 + 9x) * (9 + 6x)
(-8(9 + 6x) + 9x * (9 + 6x)) = 0
((9 * -8 + 6x * -8) + 9x * (9 + 6x)) = 0
((-72 + -48x) + 9x * (9 + 6x)) = 0
(-72 + -48x + (9 * 9x + 6x * 9x)) = 0
(-72 + -48x + (81x + 54x2)) = 0

Combine like terms: -48x + 81x = 33x
(-72 + 33x + 54x2) = 0

Solving
-72 + 33x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 11x + 18x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 0.8888888889}

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