(6x-3)(5x+3)=0

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Solution for (6x-3)(5x+3)=0 equation: 


Simplifying
(6x + -3)(5x + 3) = 0

Reorder the terms:
(-3 + 6x)(5x + 3) = 0

Reorder the terms:
(-3 + 6x)(3 + 5x) = 0

Multiply (-3 + 6x) * (3 + 5x)
(-3(3 + 5x) + 6x * (3 + 5x)) = 0
((3 * -3 + 5x * -3) + 6x * (3 + 5x)) = 0
((-9 + -15x) + 6x * (3 + 5x)) = 0
(-9 + -15x + (3 * 6x + 5x * 6x)) = 0
(-9 + -15x + (18x + 30x2)) = 0

Combine like terms: -15x + 18x = 3x
(-9 + 3x + 30x2) = 0

Solving
-9 + 3x + 30x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.6, 0.5}

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