(3x-15)(x+7)=0

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Solution for (3x-15)(x+7)=0 equation: 


Simplifying
(3x + -15)(x + 7) = 0

Reorder the terms:
(-15 + 3x)(x + 7) = 0

Reorder the terms:
(-15 + 3x)(7 + x) = 0

Multiply (-15 + 3x) * (7 + x)
(-15(7 + x) + 3x * (7 + x)) = 0
((7 * -15 + x * -15) + 3x * (7 + x)) = 0
((-105 + -15x) + 3x * (7 + x)) = 0
(-105 + -15x + (7 * 3x + x * 3x)) = 0
(-105 + -15x + (21x + 3x2)) = 0

Combine like terms: -15x + 21x = 6x
(-105 + 6x + 3x2) = 0

Solving
-105 + 6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 2x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 5}

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