(5x+3)*(24-3x)=0

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Solution for (5x+3)*(24-3x)=0 equation: 


Simplifying
(5x + 3)(24 + -3x) = 0

Reorder the terms:
(3 + 5x)(24 + -3x) = 0

Multiply (3 + 5x) * (24 + -3x)
(3(24 + -3x) + 5x * (24 + -3x)) = 0
((24 * 3 + -3x * 3) + 5x * (24 + -3x)) = 0
((72 + -9x) + 5x * (24 + -3x)) = 0
(72 + -9x + (24 * 5x + -3x * 5x)) = 0
(72 + -9x + (120x + -15x2)) = 0

Combine like terms: -9x + 120x = 111x
(72 + 111x + -15x2) = 0

Solving
72 + 111x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 37x + -5x2) = 0

Factor a trinomial.
3((8 + -1x)(3 + 5x)) = 0

Ignore the factor 3.

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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6
Solution
x = {8, -0.6}

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