(2x+8)(3x+24)=0

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Solution for (2x+8)(3x+24)=0 equation: 


Simplifying
(2x + 8)(3x + 24) = 0

Reorder the terms:
(8 + 2x)(3x + 24) = 0

Reorder the terms:
(8 + 2x)(24 + 3x) = 0

Multiply (8 + 2x) * (24 + 3x)
(8(24 + 3x) + 2x * (24 + 3x)) = 0
((24 * 8 + 3x * 8) + 2x * (24 + 3x)) = 0
((192 + 24x) + 2x * (24 + 3x)) = 0
(192 + 24x + (24 * 2x + 3x * 2x)) = 0
(192 + 24x + (48x + 6x2)) = 0

Combine like terms: 24x + 48x = 72x
(192 + 72x + 6x2) = 0

Solving
192 + 72x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(32 + 12x + x2) = 0

Factor a trinomial.
6((8 + x)(4 + x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {-8, -4}

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