-16t^2-28t+150=0

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Solution for -16t^2-28t+150=0 equation: 


Simplifying
-16t2 + -28t + 150 = 0

Reorder the terms:
150 + -28t + -16t2 = 0

Solving
150 + -28t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -14t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -14t + -8t2)' equal to zero and attempt to solve:

Simplifying
75 + -14t + -8t2 = 0

Solving
75 + -14t + -8t2 = 0

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

Divide each side by '-8'.
-9.375 + 1.75t + t2 = 0

Move the constant term to the right:

Add '9.375' to each side of the equation.
-9.375 + 1.75t + 9.375 + t2 = 0 + 9.375

Reorder the terms:
-9.375 + 9.375 + 1.75t + t2 = 0 + 9.375

Combine like terms: -9.375 + 9.375 = 0.000
0.000 + 1.75t + t2 = 0 + 9.375
1.75t + t2 = 0 + 9.375

Combine like terms: 0 + 9.375 = 9.375
1.75t + t2 = 9.375

The t term is 1.75t.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75t + 0.765625 + t2 = 9.375 + 0.765625

Reorder the terms:
0.765625 + 1.75t + t2 = 9.375 + 0.765625

Combine like terms: 9.375 + 0.765625 = 10.140625
0.765625 + 1.75t + t2 = 10.140625

Factor a perfect square on the left side:
(t + 0.875)(t + 0.875) = 10.140625

Calculate the square root of the right side: 3.184434801

Break this problem into two subproblems by setting 
(t + 0.875) equal to 3.184434801 and -3.184434801.


Subproblem 1
t + 0.875 = 3.184434801

Simplifying
t + 0.875 = 3.184434801

Reorder the terms:
0.875 + t = 3.184434801

Solving
0.875 + t = 3.184434801

Solving for variable 't'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + t = 3.184434801 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + t = 3.184434801 + -0.875
t = 3.184434801 + -0.875

Combine like terms: 3.184434801 + -0.875 = 2.309434801
t = 2.309434801

Simplifying
t = 2.309434801


Subproblem 2
t + 0.875 = -3.184434801

Simplifying
t + 0.875 = -3.184434801

Reorder the terms:
0.875 + t = -3.184434801

Solving
0.875 + t = -3.184434801

Solving for variable 't'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + t = -3.184434801 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + t = -3.184434801 + -0.875
t = -3.184434801 + -0.875

Combine like terms: -3.184434801 + -0.875 = -4.059434801
t = -4.059434801

Simplifying
t = -4.059434801


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.309434801, -4.059434801}
Solution
t = {2.309434801, -4.059434801}

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