114=-38t^2+152t

Solution for 114=-38t^2+152t equation:

Simplifying
114 = -38t2 + 152t

Reorder the terms:
114 = 152t + -38t2

Solving
114 = 152t + -38t2

Solving for variable 't'.

Reorder the terms:
114 + -152t + 38t2 = 152t + -152t + -38t2 + 38t2

Combine like terms: 152t + -152t = 0
114 + -152t + 38t2 = 0 + -38t2 + 38t2
114 + -152t + 38t2 = -38t2 + 38t2

Combine like terms: -38t2 + 38t2 = 0
114 + -152t + 38t2 = 0

Factor out the Greatest Common Factor (GCF), '38'.
38(3 + -4t + t2) = 0

Factor a trinomial.
38((1 + -1t)(3 + -1t)) = 0

Ignore the factor 38.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
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 = {1, 3}