-4(4t^2-5t-75)=304

Solution for -4(4t^2-5t-75)=304 equation:

Simplifying
-4(4t2 + -5t + -75) = 304

Reorder the terms:
-4(-75 + -5t + 4t2) = 304
(-75 * -4 + -5t * -4 + 4t2 * -4) = 304
(300 + 20t + -16t2) = 304

Solving
300 + 20t + -16t2 = 304

Solving for variable 't'.

Reorder the terms:
300 + -304 + 20t + -16t2 = 304 + -304

Combine like terms: 300 + -304 = -4
-4 + 20t + -16t2 = 304 + -304

Combine like terms: 304 + -304 = 0
-4 + 20t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5t + -4t2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
Solution
t = {1, 0.25}