25-q^2=2q+1

Solution for 25-q^2=2q+1 equation:

Simplifying
25 + -1q2 = 2q + 1

Reorder the terms:
25 + -1q2 = 1 + 2q

Solving
25 + -1q2 = 1 + 2q

Solving for variable 'q'.

Reorder the terms:
25 + -1 + -2q + -1q2 = 1 + 2q + -1 + -2q

Combine like terms: 25 + -1 = 24
24 + -2q + -1q2 = 1 + 2q + -1 + -2q

Reorder the terms:
24 + -2q + -1q2 = 1 + -1 + 2q + -2q

Combine like terms: 1 + -1 = 0
24 + -2q + -1q2 = 0 + 2q + -2q
24 + -2q + -1q2 = 2q + -2q

Combine like terms: 2q + -2q = 0
24 + -2q + -1q2 = 0

Factor a trinomial.
(4 + -1q)(6 + q) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + q)' equal to zero and attempt to solve:

Simplifying
6 + q = 0

Solving
6 + q = 0

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

Add '-6' to each side of the equation.
6 + -6 + q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + q = 0 + -6
q = 0 + -6

Combine like terms: 0 + -6 = -6
q = -6

Simplifying
q = -6
Solution
q = {4, -6}