-490t^2+1470t+960=0

Solution for -490t^2+1470t+960=0 equation:

Simplifying
-490t2 + 1470t + 960 = 0

Reorder the terms:
960 + 1470t + -490t2 = 0

Solving
960 + 1470t + -490t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(96 + 147t + -49t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(96 + 147t + -49t2)' equal to zero and attempt to solve:

Simplifying
96 + 147t + -49t2 = 0

Solving
96 + 147t + -49t2 = 0

Begin completing the square.  Divide all terms by
-49 the coefficient of the squared term: 

Divide each side by '-49'.
-1.959183673 + -3t + t2 = 0

Move the constant term to the right:

Add '1.959183673' to each side of the equation.
-1.959183673 + -3t + 1.959183673 + t2 = 0 + 1.959183673

Reorder the terms:
-1.959183673 + 1.959183673 + -3t + t2 = 0 + 1.959183673

Combine like terms: -1.959183673 + 1.959183673 = 0.000000000
0.000000000 + -3t + t2 = 0 + 1.959183673
-3t + t2 = 0 + 1.959183673

Combine like terms: 0 + 1.959183673 = 1.959183673
-3t + t2 = 1.959183673

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 1.959183673 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 1.959183673 + 2.25

Combine like terms: 1.959183673 + 2.25 = 4.209183673
2.25 + -3t + t2 = 4.209183673

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 4.209183673

Calculate the square root of the right side: 2.051629517

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.051629517 and -2.051629517.

Subproblem 1
t + -1.5 = 2.051629517

Simplifying
t + -1.5 = 2.051629517

Reorder the terms:
-1.5 + t = 2.051629517

Solving
-1.5 + t = 2.051629517

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 2.051629517 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.051629517 + 1.5
t = 2.051629517 + 1.5

Combine like terms: 2.051629517 + 1.5 = 3.551629517
t = 3.551629517

Simplifying
t = 3.551629517

Subproblem 2
t + -1.5 = -2.051629517

Simplifying
t + -1.5 = -2.051629517

Reorder the terms:
-1.5 + t = -2.051629517

Solving
-1.5 + t = -2.051629517

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -2.051629517 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.051629517 + 1.5
t = -2.051629517 + 1.5

Combine like terms: -2.051629517 + 1.5 = -0.551629517
t = -0.551629517

Simplifying
t = -0.551629517

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.551629517, -0.551629517}
Solution
t = {3.551629517, -0.551629517}