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

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


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

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

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

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

Combine like terms: -30x + 36x = 6x
(-45 + 6x + 24x2) = 0

Solving
-45 + 6x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2x + 8x2) = 0

Factor a trinomial.
3((-3 + -2x)(5 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
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

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 = {-1.5, 1.25}

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