5(x+3)(3x+8)=0

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Solution for 5(x+3)(3x+8)=0 equation: 


Simplifying
5(x + 3)(3x + 8) = 0

Reorder the terms:
5(3 + x)(3x + 8) = 0

Reorder the terms:
5(3 + x)(8 + 3x) = 0

Multiply (3 + x) * (8 + 3x)
5(3(8 + 3x) + x(8 + 3x)) = 0
5((8 * 3 + 3x * 3) + x(8 + 3x)) = 0
5((24 + 9x) + x(8 + 3x)) = 0
5(24 + 9x + (8 * x + 3x * x)) = 0
5(24 + 9x + (8x + 3x2)) = 0

Combine like terms: 9x + 8x = 17x
5(24 + 17x + 3x2) = 0
(24 * 5 + 17x * 5 + 3x2 * 5) = 0
(120 + 85x + 15x2) = 0

Solving
120 + 85x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + 17x + 3x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 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 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {-3, -2.666666667}

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