45q^2+22q-3=0

Solution for 45q^2+22q-3=0 equation:

Simplifying
45q2 + 22q + -3 = 0

Reorder the terms:
-3 + 22q + 45q2 = 0

Solving
-3 + 22q + 45q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-3 + -5q)(1 + -9q) = 0

Subproblem 1
Set the factor '(-3 + -5q)' equal to zero and attempt to solve:

Simplifying
-3 + -5q = 0

Solving
-3 + -5q = 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 + -5q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5q = 0 + 3
-5q = 0 + 3

Combine like terms: 0 + 3 = 3
-5q = 3

Divide each side by '-5'.
q = -0.6

Simplifying
q = -0.6
Subproblem 2
Set the factor '(1 + -9q)' equal to zero and attempt to solve:

Simplifying
1 + -9q = 0

Solving
1 + -9q = 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 + -9q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9q = 0 + -1
-9q = 0 + -1

Combine like terms: 0 + -1 = -1
-9q = -1

Divide each side by '-9'.
q = 0.1111111111

Simplifying
q = 0.1111111111
Solution
q = {-0.6, 0.1111111111}