(8x-9)(9x+3)=0

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Solution for (8x-9)(9x+3)=0 equation: 


Simplifying
(8x + -9)(9x + 3) = 0

Reorder the terms:
(-9 + 8x)(9x + 3) = 0

Reorder the terms:
(-9 + 8x)(3 + 9x) = 0

Multiply (-9 + 8x) * (3 + 9x)
(-9(3 + 9x) + 8x * (3 + 9x)) = 0
((3 * -9 + 9x * -9) + 8x * (3 + 9x)) = 0
((-27 + -81x) + 8x * (3 + 9x)) = 0
(-27 + -81x + (3 * 8x + 9x * 8x)) = 0
(-27 + -81x + (24x + 72x2)) = 0

Combine like terms: -81x + 24x = -57x
(-27 + -57x + 72x2) = 0

Solving
-27 + -57x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -19x + 24x2) = 0

Factor a trinomial.
3((-1 + -3x)(9 + -8x)) = 0

Ignore the factor 3.

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
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
Solution
x = {-0.3333333333, 1.125}

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