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

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


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

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

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

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

Combine like terms: 6x + -15x = -9x
(-30 + -9x + 3x2) = 0

Solving
-30 + -9x + 3x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3((-2 + -1x)(5 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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