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

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


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

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

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

Multiply (6 + 2x) * (-5 + 2x)
(6(-5 + 2x) + 2x * (-5 + 2x)) = 0
((-5 * 6 + 2x * 6) + 2x * (-5 + 2x)) = 0
((-30 + 12x) + 2x * (-5 + 2x)) = 0
(-30 + 12x + (-5 * 2x + 2x * 2x)) = 0
(-30 + 12x + (-10x + 4x2)) = 0

Combine like terms: 12x + -10x = 2x
(-30 + 2x + 4x2) = 0

Solving
-30 + 2x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-3, 2.5}

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