5q^2(4q-5)(2q-5)=

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Solution for 5q^2(4q-5)(2q-5)= equation: 


Simplifying
5q2(4q + -5)(2q + -5) = 0

Reorder the terms:
5q2(-5 + 4q)(2q + -5) = 0

Reorder the terms:
5q2(-5 + 4q)(-5 + 2q) = 0

Multiply (-5 + 4q) * (-5 + 2q)
5q2(-5(-5 + 2q) + 4q * (-5 + 2q)) = 0
5q2((-5 * -5 + 2q * -5) + 4q * (-5 + 2q)) = 0
5q2((25 + -10q) + 4q * (-5 + 2q)) = 0
5q2(25 + -10q + (-5 * 4q + 2q * 4q)) = 0
5q2(25 + -10q + (-20q + 8q2)) = 0

Combine like terms: -10q + -20q = -30q
5q2(25 + -30q + 8q2) = 0
(25 * 5q2 + -30q * 5q2 + 8q2 * 5q2) = 0
(125q2 + -150q3 + 40q4) = 0

Solving
125q2 + -150q3 + 40q4 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '5q2'.
5q2(25 + -30q + 8q2) = 0

Factor a trinomial.
5q2((5 + -4q)(5 + -2q)) = 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 '(5 + -4q)' equal to zero and attempt to solve:

Simplifying
5 + -4q = 0

Solving
5 + -4q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4q = 0 + -5
-4q = 0 + -5

Combine like terms: 0 + -5 = -5
-4q = -5

Divide each side by '-4'.
q = 1.25

Simplifying
q = 1.25

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

Simplifying
5 + -2q = 0

Solving
5 + -2q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2q = 0 + -5
-2q = 0 + -5

Combine like terms: 0 + -5 = -5
-2q = -5

Divide each side by '-2'.
q = 2.5

Simplifying
q = 2.5
Solution
q = {0, 1.25, 2.5}

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