4(-4t^2+16t-7)=0

Solution for 4(-4t^2+16t-7)=0 equation:

Simplifying
4(-4t2 + 16t + -7) = 0

Reorder the terms:
4(-7 + 16t + -4t2) = 0
(-7 * 4 + 16t * 4 + -4t2 * 4) = 0
(-28 + 64t + -16t2) = 0

Solving
-28 + 64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 16t + -4t2) = 0

Factor a trinomial.
4((-7 + 2t)(1 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + 2t)' equal to zero and attempt to solve:

Simplifying
-7 + 2t = 0

Solving
-7 + 2t = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2t = 0 + 7
2t = 0 + 7

Combine like terms: 0 + 7 = 7
2t = 7

Divide each side by '2'.
t = 3.5

Simplifying
t = 3.5
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {3.5, 0.5}