100=64+24t+-4t^2

Solution for 100=64+24t+-4t^2 equation:

Simplifying
100 = 64 + 24t + -4t2

Solving
100 = 64 + 24t + -4t2

Solving for variable 't'.

Combine like terms: 100 + -64 = 36
36 + -24t + 4t2 = 64 + 24t + -4t2 + -64 + -24t + 4t2

Reorder the terms:
36 + -24t + 4t2 = 64 + -64 + 24t + -24t + -4t2 + 4t2

Combine like terms: 64 + -64 = 0
36 + -24t + 4t2 = 0 + 24t + -24t + -4t2 + 4t2
36 + -24t + 4t2 = 24t + -24t + -4t2 + 4t2

Combine like terms: 24t + -24t = 0
36 + -24t + 4t2 = 0 + -4t2 + 4t2
36 + -24t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
36 + -24t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6t + t2) = 0

Factor a trinomial.
4((3 + -1t)(3 + -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 '(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
Solution
t = {3, 3}