(8x+15)(3x+24)=0

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Solution for (8x+15)(3x+24)=0 equation: 


Simplifying
(8x + 15)(3x + 24) = 0

Reorder the terms:
(15 + 8x)(3x + 24) = 0

Reorder the terms:
(15 + 8x)(24 + 3x) = 0

Multiply (15 + 8x) * (24 + 3x)
(15(24 + 3x) + 8x * (24 + 3x)) = 0
((24 * 15 + 3x * 15) + 8x * (24 + 3x)) = 0
((360 + 45x) + 8x * (24 + 3x)) = 0
(360 + 45x + (24 * 8x + 3x * 8x)) = 0
(360 + 45x + (192x + 24x2)) = 0

Combine like terms: 45x + 192x = 237x
(360 + 237x + 24x2) = 0

Solving
360 + 237x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(120 + 79x + 8x2) = 0

Factor a trinomial.
3((8 + x)(15 + 8x)) = 0

Ignore the factor 3.

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 '(15 + 8x)' equal to zero and attempt to solve:

Simplifying
15 + 8x = 0

Solving
15 + 8x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 8x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8x = 0 + -15
8x = 0 + -15

Combine like terms: 0 + -15 = -15
8x = -15

Divide each side by '8'.
x = -1.875

Simplifying
x = -1.875
Solution
x = {-8, -1.875}

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