-8(2t^2-13t)=48

Solution for -8(2t^2-13t)=48 equation:

Simplifying
-8(2t2 + -13t) = 48

Reorder the terms:
-8(-13t + 2t2) = 48
(-13t * -8 + 2t2 * -8) = 48
(104t + -16t2) = 48

Solving
104t + -16t2 = 48

Solving for variable 't'.

Reorder the terms:
-48 + 104t + -16t2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 104t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + 13t + -2t2) = 0

Factor a trinomial.
8((-6 + t)(1 + -2t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 0

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

Add '6' to each side of the equation.
-6 + 6 + t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + t = 0 + 6
t = 0 + 6

Combine like terms: 0 + 6 = 6
t = 6

Simplifying
t = 6
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 = {6, 0.5}