4t^2=8t-3

Solution for 4t^2=8t-3 equation:

Simplifying
4t2 = 8t + -3

Reorder the terms:
4t2 = -3 + 8t

Solving
4t2 = -3 + 8t

Solving for variable 't'.

Reorder the terms:
3 + -8t + 4t2 = -3 + 8t + 3 + -8t

Reorder the terms:
3 + -8t + 4t2 = -3 + 3 + 8t + -8t

Combine like terms: -3 + 3 = 0
3 + -8t + 4t2 = 0 + 8t + -8t
3 + -8t + 4t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
3 + -8t + 4t2 = 0

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