(2x+8)(3x-15)=0

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Solution for (2x+8)(3x-15)=0 equation: 


Simplifying
(2x + 8)(3x + -15) = 0

Reorder the terms:
(8 + 2x)(3x + -15) = 0

Reorder the terms:
(8 + 2x)(-15 + 3x) = 0

Multiply (8 + 2x) * (-15 + 3x)
(8(-15 + 3x) + 2x * (-15 + 3x)) = 0
((-15 * 8 + 3x * 8) + 2x * (-15 + 3x)) = 0
((-120 + 24x) + 2x * (-15 + 3x)) = 0
(-120 + 24x + (-15 * 2x + 3x * 2x)) = 0
(-120 + 24x + (-30x + 6x2)) = 0

Combine like terms: 24x + -30x = -6x
(-120 + -6x + 6x2) = 0

Solving
-120 + -6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + -1x + x2) = 0

Factor a trinomial.
6((-4 + -1x)(5 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 5}

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