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

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


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

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

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

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

Combine like terms: -45x + 54x = 9x
(-81 + 9x + 30x2) = 0

Solving
-81 + 9x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + 3x + 10x2) = 0

Factor a trinomial.
3((-9 + -5x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
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

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 = {-1.8, 1.5}

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