(2t-3)(2t+1)=5

Solution for (2t-3)(2t+1)=5 equation:

Simplifying
(2t + -3)(2t + 1) = 5

Reorder the terms:
(-3 + 2t)(2t + 1) = 5

Reorder the terms:
(-3 + 2t)(1 + 2t) = 5

Multiply (-3 + 2t) * (1 + 2t)
(-3(1 + 2t) + 2t * (1 + 2t)) = 5
((1 * -3 + 2t * -3) + 2t * (1 + 2t)) = 5
((-3 + -6t) + 2t * (1 + 2t)) = 5
(-3 + -6t + (1 * 2t + 2t * 2t)) = 5
(-3 + -6t + (2t + 4t2)) = 5

Combine like terms: -6t + 2t = -4t
(-3 + -4t + 4t2) = 5

Solving
-3 + -4t + 4t2 = 5

Solving for variable 't'.

Reorder the terms:
-3 + -5 + -4t + 4t2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -4t + 4t2 = 5 + -5

Combine like terms: 5 + -5 = 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}