(2t+t-6)(2t+2t-1)=

Solution for (2t+t-6)(2t+2t-1)= equation:

Simplifying
(2t + t + -6)(2t + 2t + -1) = 0

Reorder the terms:
(-6 + 2t + t)(2t + 2t + -1) = 0

Combine like terms: 2t + t = 3t
(-6 + 3t)(2t + 2t + -1) = 0

Reorder the terms:
(-6 + 3t)(-1 + 2t + 2t) = 0

Combine like terms: 2t + 2t = 4t
(-6 + 3t)(-1 + 4t) = 0

Multiply (-6 + 3t) * (-1 + 4t)
(-6(-1 + 4t) + 3t * (-1 + 4t)) = 0
((-1 * -6 + 4t * -6) + 3t * (-1 + 4t)) = 0
((6 + -24t) + 3t * (-1 + 4t)) = 0
(6 + -24t + (-1 * 3t + 4t * 3t)) = 0
(6 + -24t + (-3t + 12t2)) = 0

Combine like terms: -24t + -3t = -27t
(6 + -27t + 12t2) = 0

Solving
6 + -27t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -9t + 4t2) = 0

Factor a trinomial.
3((1 + -4t)(2 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
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 = {0.25, 2}