40(t)=-16t^2+150

Solution for 40(t)=-16t^2+150 equation:

Simplifying
40(t) = -16t2 + 150

Reorder the terms:
40t = 150 + -16t2

Solving
40t = 150 + -16t2

Solving for variable 't'.

Reorder the terms:
-150 + 40t + 16t2 = 150 + -16t2 + -150 + 16t2

Reorder the terms:
-150 + 40t + 16t2 = 150 + -150 + -16t2 + 16t2

Combine like terms: 150 + -150 = 0
-150 + 40t + 16t2 = 0 + -16t2 + 16t2
-150 + 40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-150 + 40t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + 20t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-75 + 20t + 8t2)' equal to zero and attempt to solve:

Simplifying
-75 + 20t + 8t2 = 0

Solving
-75 + 20t + 8t2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-9.375 + 2.5t + t2 = 0

Move the constant term to the right:

Add '9.375' to each side of the equation.
-9.375 + 2.5t + 9.375 + t2 = 0 + 9.375

Reorder the terms:
-9.375 + 9.375 + 2.5t + t2 = 0 + 9.375

Combine like terms: -9.375 + 9.375 = 0.000
0.000 + 2.5t + t2 = 0 + 9.375
2.5t + t2 = 0 + 9.375

Combine like terms: 0 + 9.375 = 9.375
2.5t + t2 = 9.375

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = 9.375 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 9.375 + 1.5625

Combine like terms: 9.375 + 1.5625 = 10.9375
1.5625 + 2.5t + t2 = 10.9375

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 10.9375

Calculate the square root of the right side: 3.307189139

Break this problem into two subproblems by setting 
(t + 1.25) equal to 3.307189139 and -3.307189139.

Subproblem 1
t + 1.25 = 3.307189139

Simplifying
t + 1.25 = 3.307189139

Reorder the terms:
1.25 + t = 3.307189139

Solving
1.25 + t = 3.307189139

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 3.307189139 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 3.307189139 + -1.25
t = 3.307189139 + -1.25

Combine like terms: 3.307189139 + -1.25 = 2.057189139
t = 2.057189139

Simplifying
t = 2.057189139

Subproblem 2
t + 1.25 = -3.307189139

Simplifying
t + 1.25 = -3.307189139

Reorder the terms:
1.25 + t = -3.307189139

Solving
1.25 + t = -3.307189139

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -3.307189139 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -3.307189139 + -1.25
t = -3.307189139 + -1.25

Combine like terms: -3.307189139 + -1.25 = -4.557189139
t = -4.557189139

Simplifying
t = -4.557189139

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.057189139, -4.557189139}
Solution
t = {2.057189139, -4.557189139}