10t^2=13t-4

Solution for 10t^2=13t-4 equation:

Simplifying
10t2 = 13t + -4

Reorder the terms:
10t2 = -4 + 13t

Solving
10t2 = -4 + 13t

Solving for variable 't'.

Reorder the terms:
4 + -13t + 10t2 = -4 + 13t + 4 + -13t

Reorder the terms:
4 + -13t + 10t2 = -4 + 4 + 13t + -13t

Combine like terms: -4 + 4 = 0
4 + -13t + 10t2 = 0 + 13t + -13t
4 + -13t + 10t2 = 13t + -13t

Combine like terms: 13t + -13t = 0
4 + -13t + 10t2 = 0

Factor a trinomial.
(1 + -2t)(4 + -5t) = 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 '(4 + -5t)' equal to zero and attempt to solve:

Simplifying
4 + -5t = 0

Solving
4 + -5t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5t = 0 + -4
-5t = 0 + -4

Combine like terms: 0 + -4 = -4
-5t = -4

Divide each side by '-5'.
t = 0.8

Simplifying
t = 0.8
Solution
t = {0.5, 0.8}