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

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


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

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

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

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

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

Solving
-54 + 33x + 72x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

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

Simplifying
-9 + -8x = 0

Solving
-9 + -8x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -8x = 0 + 9

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

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

Divide each side by '-8'.
x = -1.125

Simplifying
x = -1.125

Subproblem 2
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
Solution
x = {-1.125, 0.6666666667}

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