(2t-1)(2t-1)=9

Solution for (2t-1)(2t-1)=9 equation:

Simplifying
(2t + -1)(2t + -1) = 9

Reorder the terms:
(-1 + 2t)(2t + -1) = 9

Reorder the terms:
(-1 + 2t)(-1 + 2t) = 9

Multiply (-1 + 2t) * (-1 + 2t)
(-1(-1 + 2t) + 2t * (-1 + 2t)) = 9
((-1 * -1 + 2t * -1) + 2t * (-1 + 2t)) = 9
((1 + -2t) + 2t * (-1 + 2t)) = 9
(1 + -2t + (-1 * 2t + 2t * 2t)) = 9
(1 + -2t + (-2t + 4t2)) = 9

Combine like terms: -2t + -2t = -4t
(1 + -4t + 4t2) = 9

Solving
1 + -4t + 4t2 = 9

Solving for variable 't'.

Reorder the terms:
1 + -9 + -4t + 4t2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + -4t + 4t2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + -4t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1t + t2) = 0

Factor a trinomial.
4((-1 + -1t)(2 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve:

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t = 0 + 1
-1t = 0 + 1

Combine like terms: 0 + 1 = 1
-1t = 1

Divide each side by '-1'.
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-1, 2}