4t^2+10t-900=0

Solution for 4t^2+10t-900=0 equation:

Simplifying
4t2 + 10t + -900 = 0

Reorder the terms:
-900 + 10t + 4t2 = 0

Solving
-900 + 10t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-450 + 5t + 2t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-450 + 5t + 2t2)' equal to zero and attempt to solve:

Simplifying
-450 + 5t + 2t2 = 0

Solving
-450 + 5t + 2t2 = 0

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

Divide each side by '2'.
-225 + 2.5t + t2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 2.5t + 225 + t2 = 0 + 225

Reorder the terms:
-225 + 225 + 2.5t + t2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 2.5t + t2 = 0 + 225
2.5t + t2 = 0 + 225

Combine like terms: 0 + 225 = 225
2.5t + t2 = 225

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 = 225 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 225 + 1.5625

Combine like terms: 225 + 1.5625 = 226.5625
1.5625 + 2.5t + t2 = 226.5625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 226.5625

Calculate the square root of the right side: 15.051993223

Break this problem into two subproblems by setting 
(t + 1.25) equal to 15.051993223 and -15.051993223.

Subproblem 1
t + 1.25 = 15.051993223

Simplifying
t + 1.25 = 15.051993223

Reorder the terms:
1.25 + t = 15.051993223

Solving
1.25 + t = 15.051993223

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 = 15.051993223 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 15.051993223 + -1.25
t = 15.051993223 + -1.25

Combine like terms: 15.051993223 + -1.25 = 13.801993223
t = 13.801993223

Simplifying
t = 13.801993223

Subproblem 2
t + 1.25 = -15.051993223

Simplifying
t + 1.25 = -15.051993223

Reorder the terms:
1.25 + t = -15.051993223

Solving
1.25 + t = -15.051993223

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 = -15.051993223 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -15.051993223 + -1.25
t = -15.051993223 + -1.25

Combine like terms: -15.051993223 + -1.25 = -16.301993223
t = -16.301993223

Simplifying
t = -16.301993223

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.801993223, -16.301993223}
Solution
t = {13.801993223, -16.301993223}