16t^2+4t=420

Solution for 16t^2+4t=420 equation:

Simplifying
16t2 + 4t = 420

Reorder the terms:
4t + 16t2 = 420

Solving
4t + 16t2 = 420

Solving for variable 't'.

Reorder the terms:
-420 + 4t + 16t2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + 4t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-105 + t + 4t2) = 0

Factor a trinomial.
4((-21 + -4t)(5 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-21 + -4t)' equal to zero and attempt to solve:

Simplifying
-21 + -4t = 0

Solving
-21 + -4t = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4t = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4t = 0 + 21
-4t = 0 + 21

Combine like terms: 0 + 21 = 21
-4t = 21

Divide each side by '-4'.
t = -5.25

Simplifying
t = -5.25
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-5.25, 5}