8t^2=2t+3

Solution for 8t^2=2t+3 equation:

Simplifying
8t2 = 2t + 3

Reorder the terms:
8t2 = 3 + 2t

Solving
8t2 = 3 + 2t

Solving for variable 't'.

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

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

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

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

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

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 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
Solution
t = {-0.5, 0.75}