(5x-8)(9x+6)=0

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Solution for (5x-8)(9x+6)=0 equation: 


Simplifying
(5x + -8)(9x + 6) = 0

Reorder the terms:
(-8 + 5x)(9x + 6) = 0

Reorder the terms:
(-8 + 5x)(6 + 9x) = 0

Multiply (-8 + 5x) * (6 + 9x)
(-8(6 + 9x) + 5x * (6 + 9x)) = 0
((6 * -8 + 9x * -8) + 5x * (6 + 9x)) = 0
((-48 + -72x) + 5x * (6 + 9x)) = 0
(-48 + -72x + (6 * 5x + 9x * 5x)) = 0
(-48 + -72x + (30x + 45x2)) = 0

Combine like terms: -72x + 30x = -42x
(-48 + -42x + 45x2) = 0

Solving
-48 + -42x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + -14x + 15x2) = 0

Factor a trinomial.
3((-2 + -3x)(8 + -5x)) = 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 '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-0.6666666667, 1.6}

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