5q(q-2)=15

Solution for 5q(q-2)=15 equation:

Simplifying
5q(q + -2) = 15

Reorder the terms:
5q(-2 + q) = 15
(-2 * 5q + q * 5q) = 15
(-10q + 5q2) = 15

Solving
-10q + 5q2 = 15

Solving for variable 'q'.

Reorder the terms:
-15 + -10q + 5q2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -10q + 5q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2q + q2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -1q)' equal to zero and attempt to solve:

Simplifying
-1 + -1q = 0

Solving
-1 + -1q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1q = 0 + 1
-1q = 0 + 1

Combine like terms: 0 + 1 = 1
-1q = 1

Divide each side by '-1'.
q = -1

Simplifying
q = -1
Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Solution
q = {-1, 3}