(3x+6)(2x-5)=0

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Solution for (3x+6)(2x-5)=0 equation: 


Simplifying
(3x + 6)(2x + -5) = 0

Reorder the terms:
(6 + 3x)(2x + -5) = 0

Reorder the terms:
(6 + 3x)(-5 + 2x) = 0

Multiply (6 + 3x) * (-5 + 2x)
(6(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * 6 + 2x * 6) + 3x * (-5 + 2x)) = 0
((-30 + 12x) + 3x * (-5 + 2x)) = 0
(-30 + 12x + (-5 * 3x + 2x * 3x)) = 0
(-30 + 12x + (-15x + 6x2)) = 0

Combine like terms: 12x + -15x = -3x
(-30 + -3x + 6x2) = 0

Solving
-30 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1x + 2x2) = 0

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

Ignore the factor 3.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 2.5}

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