0=64t^2+64t-48

Solution for 0=64t^2+64t-48 equation:

Simplifying
0 = 64t2 + 64t + -48

Reorder the terms:
0 = -48 + 64t + 64t2

Solving
0 = -48 + 64t + 64t2

Solving for variable 't'.

Combine like terms: 0 + 48 = 48
48 + -64t + -64t2 = -48 + 64t + 64t2 + 48 + -64t + -64t2

Reorder the terms:
48 + -64t + -64t2 = -48 + 48 + 64t + -64t + 64t2 + -64t2

Combine like terms: -48 + 48 = 0
48 + -64t + -64t2 = 0 + 64t + -64t + 64t2 + -64t2
48 + -64t + -64t2 = 64t + -64t + 64t2 + -64t2

Combine like terms: 64t + -64t = 0
48 + -64t + -64t2 = 0 + 64t2 + -64t2
48 + -64t + -64t2 = 64t2 + -64t2

Combine like terms: 64t2 + -64t2 = 0
48 + -64t + -64t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(3 + -4t + -4t2) = 0

Factor a trinomial.
16((1 + -2t)(3 + 2t)) = 0

Ignore the factor 16.
Subproblem 1
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
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 = {0.5, -1.5}