(3x-15)(2x+22)=0

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Solution for (3x-15)(2x+22)=0 equation: 


Simplifying
(3x + -15)(2x + 22) = 0

Reorder the terms:
(-15 + 3x)(2x + 22) = 0

Reorder the terms:
(-15 + 3x)(22 + 2x) = 0

Multiply (-15 + 3x) * (22 + 2x)
(-15(22 + 2x) + 3x * (22 + 2x)) = 0
((22 * -15 + 2x * -15) + 3x * (22 + 2x)) = 0
((-330 + -30x) + 3x * (22 + 2x)) = 0
(-330 + -30x + (22 * 3x + 2x * 3x)) = 0
(-330 + -30x + (66x + 6x2)) = 0

Combine like terms: -30x + 66x = 36x
(-330 + 36x + 6x2) = 0

Solving
-330 + 36x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-55 + 6x + x2) = 0

Factor a trinomial.
6((-11 + -1x)(5 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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 = {-11, 5}

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