8t^2-12t=2t-3

Solution for 8t^2-12t=2t-3 equation:

Simplifying
8t2 + -12t = 2t + -3

Reorder the terms:
-12t + 8t2 = 2t + -3

Reorder the terms:
-12t + 8t2 = -3 + 2t

Solving
-12t + 8t2 = -3 + 2t

Solving for variable 't'.

Reorder the terms:
3 + -12t + -2t + 8t2 = -3 + 2t + 3 + -2t

Combine like terms: -12t + -2t = -14t
3 + -14t + 8t2 = -3 + 2t + 3 + -2t

Reorder the terms:
3 + -14t + 8t2 = -3 + 3 + 2t + -2t

Combine like terms: -3 + 3 = 0
3 + -14t + 8t2 = 0 + 2t + -2t
3 + -14t + 8t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
3 + -14t + 8t2 = 0

Factor a trinomial.
(1 + -4t)(3 + -2t) = 0

Subproblem 1
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
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 = {0.25, 1.5}