4q^2=20q-9

Solution for 4q^2=20q-9 equation:

Simplifying
4q2 = 20q + -9

Reorder the terms:
4q2 = -9 + 20q

Solving
4q2 = -9 + 20q

Solving for variable 'q'.

Reorder the terms:
9 + -20q + 4q2 = -9 + 20q + 9 + -20q

Reorder the terms:
9 + -20q + 4q2 = -9 + 9 + 20q + -20q

Combine like terms: -9 + 9 = 0
9 + -20q + 4q2 = 0 + 20q + -20q
9 + -20q + 4q2 = 20q + -20q

Combine like terms: 20q + -20q = 0
9 + -20q + 4q2 = 0

Factor a trinomial.
(1 + -2q)(9 + -2q) = 0

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

Simplifying
1 + -2q = 0

Solving
1 + -2q = 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 + -2q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2q = 0 + -1
-2q = 0 + -1

Combine like terms: 0 + -1 = -1
-2q = -1

Divide each side by '-2'.
q = 0.5

Simplifying
q = 0.5
Subproblem 2
Set the factor '(9 + -2q)' equal to zero and attempt to solve:

Simplifying
9 + -2q = 0

Solving
9 + -2q = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2q = 0 + -9
-2q = 0 + -9

Combine like terms: 0 + -9 = -9
-2q = -9

Divide each side by '-2'.
q = 4.5

Simplifying
q = 4.5
Solution
q = {0.5, 4.5}