5q^2(3q+8)(3q+8)=0

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Solution for 5q^2(3q+8)(3q+8)=0 equation: 


Simplifying
5q2(3q + 8)(3q + 8) = 0

Reorder the terms:
5q2(8 + 3q)(3q + 8) = 0

Reorder the terms:
5q2(8 + 3q)(8 + 3q) = 0

Multiply (8 + 3q) * (8 + 3q)
5q2(8(8 + 3q) + 3q * (8 + 3q)) = 0
5q2((8 * 8 + 3q * 8) + 3q * (8 + 3q)) = 0
5q2((64 + 24q) + 3q * (8 + 3q)) = 0
5q2(64 + 24q + (8 * 3q + 3q * 3q)) = 0
5q2(64 + 24q + (24q + 9q2)) = 0

Combine like terms: 24q + 24q = 48q
5q2(64 + 48q + 9q2) = 0
(64 * 5q2 + 48q * 5q2 + 9q2 * 5q2) = 0
(320q2 + 240q3 + 45q4) = 0

Solving
320q2 + 240q3 + 45q4 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '5q2'.
5q2(64 + 48q + 9q2) = 0

Factor a trinomial.
5q2((8 + 3q)(8 + 3q)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve:

Simplifying
q2 = 0

Solving
q2 = 0

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

Simplifying
q2 = 0

Take the square root of each side:
q = {0}

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

Simplifying
8 + 3q = 0

Solving
8 + 3q = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3q = 0 + -8

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

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

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

Simplifying
q = -2.666666667

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

Simplifying
8 + 3q = 0

Solving
8 + 3q = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3q = 0 + -8

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

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

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

Simplifying
q = -2.666666667
Solution
q = {0, -2.666666667, -2.666666667}

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