4(-4t^2+22t+1)=100

Solution for 4(-4t^2+22t+1)=100 equation:

Simplifying
4(-4t2 + 22t + 1) = 100

Reorder the terms:
4(1 + 22t + -4t2) = 100
(1 * 4 + 22t * 4 + -4t2 * 4) = 100
(4 + 88t + -16t2) = 100

Solving
4 + 88t + -16t2 = 100

Solving for variable 't'.

Reorder the terms:
4 + -100 + 88t + -16t2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + 88t + -16t2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + 88t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + 11t + -2t2) = 0

Factor a trinomial.
8((-4 + t)(3 + -2t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve:

Simplifying
-4 + t = 0

Solving
-4 + t = 0

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

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

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

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

Simplifying
t = 4
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {4, 1.5}