5q^2+12=23q

Solution for 5q^2+12=23q equation:

Simplifying
5q2 + 12 = 23q

Reorder the terms:
12 + 5q2 = 23q

Solving
12 + 5q2 = 23q

Solving for variable 'q'.

Reorder the terms:
12 + -23q + 5q2 = 23q + -23q

Combine like terms: 23q + -23q = 0
12 + -23q + 5q2 = 0

Factor a trinomial.
(3 + -5q)(4 + -1q) = 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 '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {0.6, 4}