(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((-5 + -4x)(2 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.25, 0.6666666667}

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