9q^2=8q^2-2q+15

Solution for 9q^2=8q^2-2q+15 equation:

Simplifying
9q2 = 8q2 + -2q + 15

Reorder the terms:
9q2 = 15 + -2q + 8q2

Solving
9q2 = 15 + -2q + 8q2

Solving for variable 'q'.

Reorder the terms:
-15 + 2q + 9q2 + -8q2 = 15 + -2q + 8q2 + -15 + 2q + -8q2

Combine like terms: 9q2 + -8q2 = 1q2
-15 + 2q + 1q2 = 15 + -2q + 8q2 + -15 + 2q + -8q2

Reorder the terms:
-15 + 2q + 1q2 = 15 + -15 + -2q + 2q + 8q2 + -8q2

Combine like terms: 15 + -15 = 0
-15 + 2q + 1q2 = 0 + -2q + 2q + 8q2 + -8q2
-15 + 2q + 1q2 = -2q + 2q + 8q2 + -8q2

Combine like terms: -2q + 2q = 0
-15 + 2q + 1q2 = 0 + 8q2 + -8q2
-15 + 2q + 1q2 = 8q2 + -8q2

Combine like terms: 8q2 + -8q2 = 0
-15 + 2q + 1q2 = 0

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

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

Simplifying
-5 + -1q = 0

Solving
-5 + -1q = 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 + -1q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1q = 0 + 5
-1q = 0 + 5

Combine like terms: 0 + 5 = 5
-1q = 5

Divide each side by '-1'.
q = -5

Simplifying
q = -5
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 = {-5, 3}