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

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


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

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

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

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

Combine like terms: -45x + 48x = 3x
(-72 + 3x + 30x2) = 0

Solving
-72 + 3x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + x + 10x2) = 0

Factor a trinomial.
3((-8 + -5x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.6, 1.5}

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