4t(t-1)=120

Solution for 4t(t-1)=120 equation:

Simplifying
4t(t + -1) = 120

Reorder the terms:
4t(-1 + t) = 120
(-1 * 4t + t * 4t) = 120
(-4t + 4t2) = 120

Solving
-4t + 4t2 = 120

Solving for variable 't'.

Reorder the terms:
-120 + -4t + 4t2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -4t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + -1t + t2) = 0

Factor a trinomial.
4((-5 + -1t)(6 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
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 = {-5, 6}