(6t+2)(9t-6)=

Solution for (6t+2)(9t-6)= equation:

Simplifying
(6t + 2)(9t + -6) = 0

Reorder the terms:
(2 + 6t)(9t + -6) = 0

Reorder the terms:
(2 + 6t)(-6 + 9t) = 0

Multiply (2 + 6t) * (-6 + 9t)
(2(-6 + 9t) + 6t * (-6 + 9t)) = 0
((-6 * 2 + 9t * 2) + 6t * (-6 + 9t)) = 0
((-12 + 18t) + 6t * (-6 + 9t)) = 0
(-12 + 18t + (-6 * 6t + 9t * 6t)) = 0
(-12 + 18t + (-36t + 54t2)) = 0

Combine like terms: 18t + -36t = -18t
(-12 + -18t + 54t2) = 0

Solving
-12 + -18t + 54t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -3t + 9t2) = 0

Factor a trinomial.
6((-1 + -3t)(2 + -3t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -3t)' equal to zero and attempt to solve:

Simplifying
-1 + -3t = 0

Solving
-1 + -3t = 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 + -3t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3t = 0 + 1
-3t = 0 + 1

Combine like terms: 0 + 1 = 1
-3t = 1

Divide each side by '-3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

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

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

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {-0.3333333333, 0.6666666667}