(9x-5)(6x+2)=0

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Solution for (9x-5)(6x+2)=0 equation: 


Simplifying
(9x + -5)(6x + 2) = 0

Reorder the terms:
(-5 + 9x)(6x + 2) = 0

Reorder the terms:
(-5 + 9x)(2 + 6x) = 0

Multiply (-5 + 9x) * (2 + 6x)
(-5(2 + 6x) + 9x * (2 + 6x)) = 0
((2 * -5 + 6x * -5) + 9x * (2 + 6x)) = 0
((-10 + -30x) + 9x * (2 + 6x)) = 0
(-10 + -30x + (2 * 9x + 6x * 9x)) = 0
(-10 + -30x + (18x + 54x2)) = 0

Combine like terms: -30x + 18x = -12x
(-10 + -12x + 54x2) = 0

Solving
-10 + -12x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6x + 27x2) = 0

Factor a trinomial.
2((-1 + -3x)(5 + -9x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

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

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

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

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {-0.3333333333, 0.5555555556}

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