(4x-5)(9x+6)=0

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Solution for (4x-5)(9x+6)=0 equation: 


Simplifying
(4x + -5)(9x + 6) = 0

Reorder the terms:
(-5 + 4x)(9x + 6) = 0

Reorder the terms:
(-5 + 4x)(6 + 9x) = 0

Multiply (-5 + 4x) * (6 + 9x)
(-5(6 + 9x) + 4x * (6 + 9x)) = 0
((6 * -5 + 9x * -5) + 4x * (6 + 9x)) = 0
((-30 + -45x) + 4x * (6 + 9x)) = 0
(-30 + -45x + (6 * 4x + 9x * 4x)) = 0
(-30 + -45x + (24x + 36x2)) = 0

Combine like terms: -45x + 24x = -21x
(-30 + -21x + 36x2) = 0

Solving
-30 + -21x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -7x + 12x2) = 0

Factor a trinomial.
3((-2 + -3x)(5 + -4x)) = 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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-0.6666666667, 1.25}

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