t(4t-12)=72

Solution for t(4t-12)=72 equation:

Simplifying
t(4t + -12) = 72

Reorder the terms:
t(-12 + 4t) = 72
(-12 * t + 4t * t) = 72
(-12t + 4t2) = 72

Solving
-12t + 4t2 = 72

Solving for variable 't'.

Reorder the terms:
-72 + -12t + 4t2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -12t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3t + t2) = 0

Factor a trinomial.
4((-3 + -1t)(6 + -1t)) = 0

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

Simplifying
-3 + -1t = 0

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

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

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

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-3, 6}