(2t)(2t)-2t=12

Solution for (2t)(2t)-2t=12 equation:

Simplifying
(2t)(2t) + -2t = 12

Remove parenthesis around (2t)
2t(2t) + -2t = 12

Remove parenthesis around (2t)
2t * 2t + -2t = 12

Reorder the terms for easier multiplication:
2 * 2t * t + -2t = 12

Multiply 2 * 2
4t * t + -2t = 12

Multiply t * t
4t2 + -2t = 12

Reorder the terms:
-2t + 4t2 = 12

Solving
-2t + 4t2 = 12

Solving for variable 't'.

Reorder the terms:
-12 + -2t + 4t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -2t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1t + 2t2) = 0

Factor a trinomial.
2((-3 + -2t)(2 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve:

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2t = 0 + 3
-2t = 0 + 3

Combine like terms: 0 + 3 = 3
-2t = 3

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
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 = {-1.5, 2}