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

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


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

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

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

Multiply (-5 + 6x) * (2 + 2x)
(-5(2 + 2x) + 6x * (2 + 2x)) = 0
((2 * -5 + 2x * -5) + 6x * (2 + 2x)) = 0
((-10 + -10x) + 6x * (2 + 2x)) = 0
(-10 + -10x + (2 * 6x + 2x * 6x)) = 0
(-10 + -10x + (12x + 12x2)) = 0

Combine like terms: -10x + 12x = 2x
(-10 + 2x + 12x2) = 0

Solving
-10 + 2x + 12x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((-1 + -1x)(5 + -6x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1, 0.8333333333}

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