-16t^2-4t+472=460

Solution for -16t^2-4t+472=460 equation:

Simplifying
-16t2 + -4t + 472 = 460

Reorder the terms:
472 + -4t + -16t2 = 460

Solving
472 + -4t + -16t2 = 460

Solving for variable 't'.

Reorder the terms:
472 + -460 + -4t + -16t2 = 460 + -460

Combine like terms: 472 + -460 = 12
12 + -4t + -16t2 = 460 + -460

Combine like terms: 460 + -460 = 0
12 + -4t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -1t + -4t2) = 0

Factor a trinomial.
4((3 + -4t)(1 + t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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 = 0 + -1

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

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

Simplifying
t = -1
Solution
t = {0.75, -1}