40=-16t^2+88t

Solution for 40=-16t^2+88t equation:

Simplifying
40 = -16t2 + 88t

Reorder the terms:
40 = 88t + -16t2

Solving
40 = 88t + -16t2

Solving for variable 't'.

Reorder the terms:
40 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2

Combine like terms: 88t + -88t = 0
40 + -88t + 16t2 = 0 + -16t2 + 16t2
40 + -88t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
40 + -88t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + -11t + 2t2) = 0

Factor a trinomial.
8((1 + -2t)(5 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 2
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
Solution
t = {0.5, 5}