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

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


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

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

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

Multiply (-9 + 5x) * (6 + 9x)
(-9(6 + 9x) + 5x * (6 + 9x)) = 0
((6 * -9 + 9x * -9) + 5x * (6 + 9x)) = 0
((-54 + -81x) + 5x * (6 + 9x)) = 0
(-54 + -81x + (6 * 5x + 9x * 5x)) = 0
(-54 + -81x + (30x + 45x2)) = 0

Combine like terms: -81x + 30x = -51x
(-54 + -51x + 45x2) = 0

Solving
-54 + -51x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -17x + 15x2) = 0

Factor a trinomial.
3((-2 + -3x)(9 + -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 '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {-0.6666666667, 1.8}

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