4t^2-40t=-96

Solution for 4t^2-40t=-96 equation:

Simplifying
4t2 + -40t = -96

Reorder the terms:
-40t + 4t2 = -96

Solving
-40t + 4t2 = -96

Solving for variable 't'.

Reorder the terms:
96 + -40t + 4t2 = -96 + 96

Combine like terms: -96 + 96 = 0
96 + -40t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + -10t + t2) = 0

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

Ignore the factor 4.
Subproblem 1
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
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 = {4, 6}