158=16t^2+32t

Solution for 158=16t^2+32t equation:

Simplifying
158 = 16t2 + 32t

Reorder the terms:
158 = 32t + 16t2

Solving
158 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
158 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
158 + -32t + -16t2 = 0 + 16t2 + -16t2
158 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
158 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(79 + -16t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(79 + -16t + -8t2)' equal to zero and attempt to solve:

Simplifying
79 + -16t + -8t2 = 0

Solving
79 + -16t + -8t2 = 0

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

Divide each side by '-8'.
-9.875 + 2t + t2 = 0

Move the constant term to the right:

Add '9.875' to each side of the equation.
-9.875 + 2t + 9.875 + t2 = 0 + 9.875

Reorder the terms:
-9.875 + 9.875 + 2t + t2 = 0 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + 2t + t2 = 0 + 9.875
2t + t2 = 0 + 9.875

Combine like terms: 0 + 9.875 = 9.875
2t + t2 = 9.875

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 9.875 + 1

Reorder the terms:
1 + 2t + t2 = 9.875 + 1

Combine like terms: 9.875 + 1 = 10.875
1 + 2t + t2 = 10.875

Factor a perfect square on the left side:
(t + 1)(t + 1) = 10.875

Calculate the square root of the right side: 3.29772649

Break this problem into two subproblems by setting 
(t + 1) equal to 3.29772649 and -3.29772649.

Subproblem 1
t + 1 = 3.29772649

Simplifying
t + 1 = 3.29772649

Reorder the terms:
1 + t = 3.29772649

Solving
1 + t = 3.29772649

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 3.29772649 + -1

Combine like terms: 1 + -1 = 0
0 + t = 3.29772649 + -1
t = 3.29772649 + -1

Combine like terms: 3.29772649 + -1 = 2.29772649
t = 2.29772649

Simplifying
t = 2.29772649

Subproblem 2
t + 1 = -3.29772649

Simplifying
t + 1 = -3.29772649

Reorder the terms:
1 + t = -3.29772649

Solving
1 + t = -3.29772649

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -3.29772649 + -1

Combine like terms: 1 + -1 = 0
0 + t = -3.29772649 + -1
t = -3.29772649 + -1

Combine like terms: -3.29772649 + -1 = -4.29772649
t = -4.29772649

Simplifying
t = -4.29772649

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.29772649, -4.29772649}
Solution
t = {2.29772649, -4.29772649}