(2s-1)(2s-1)=225

Solution for (2s-1)(2s-1)=225 equation:

Simplifying
(2s + -1)(2s + -1) = 225

Reorder the terms:
(-1 + 2s)(2s + -1) = 225

Reorder the terms:
(-1 + 2s)(-1 + 2s) = 225

Multiply (-1 + 2s) * (-1 + 2s)
(-1(-1 + 2s) + 2s * (-1 + 2s)) = 225
((-1 * -1 + 2s * -1) + 2s * (-1 + 2s)) = 225
((1 + -2s) + 2s * (-1 + 2s)) = 225
(1 + -2s + (-1 * 2s + 2s * 2s)) = 225
(1 + -2s + (-2s + 4s2)) = 225

Combine like terms: -2s + -2s = -4s
(1 + -4s + 4s2) = 225

Solving
1 + -4s + 4s2 = 225

Solving for variable 's'.

Reorder the terms:
1 + -225 + -4s + 4s2 = 225 + -225

Combine like terms: 1 + -225 = -224
-224 + -4s + 4s2 = 225 + -225

Combine like terms: 225 + -225 = 0
-224 + -4s + 4s2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-56 + -1s + s2) = 0

Factor a trinomial.
4((-7 + -1s)(8 + -1s)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1s)' equal to zero and attempt to solve:

Simplifying
-7 + -1s = 0

Solving
-7 + -1s = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1s = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1s = 0 + 7
-1s = 0 + 7

Combine like terms: 0 + 7 = 7
-1s = 7

Divide each side by '-1'.
s = -7

Simplifying
s = -7
Subproblem 2
Set the factor '(8 + -1s)' equal to zero and attempt to solve:

Simplifying
8 + -1s = 0

Solving
8 + -1s = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1s = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1s = 0 + -8
-1s = 0 + -8

Combine like terms: 0 + -8 = -8
-1s = -8

Divide each side by '-1'.
s = 8

Simplifying
s = 8
Solution
s = {-7, 8}