3t(t-1)=36

Solution for 3t(t-1)=36 equation:

Simplifying
3t(t + -1) = 36

Reorder the terms:
3t(-1 + t) = 36
(-1 * 3t + t * 3t) = 36
(-3t + 3t2) = 36

Solving
-3t + 3t2 = 36

Solving for variable 't'.

Reorder the terms:
-36 + -3t + 3t2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -3t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -1t + t2) = 0

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

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

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-3, 4}