(2t-1)(5t-1)=13

Solution for (2t-1)(5t-1)=13 equation:

Simplifying
(2t + -1)(5t + -1) = 13

Reorder the terms:
(-1 + 2t)(5t + -1) = 13

Reorder the terms:
(-1 + 2t)(-1 + 5t) = 13

Multiply (-1 + 2t) * (-1 + 5t)
(-1(-1 + 5t) + 2t * (-1 + 5t)) = 13
((-1 * -1 + 5t * -1) + 2t * (-1 + 5t)) = 13
((1 + -5t) + 2t * (-1 + 5t)) = 13
(1 + -5t + (-1 * 2t + 5t * 2t)) = 13
(1 + -5t + (-2t + 10t2)) = 13

Combine like terms: -5t + -2t = -7t
(1 + -7t + 10t2) = 13

Solving
1 + -7t + 10t2 = 13

Solving for variable 't'.

Reorder the terms:
1 + -13 + -7t + 10t2 = 13 + -13

Combine like terms: 1 + -13 = -12
-12 + -7t + 10t2 = 13 + -13

Combine like terms: 13 + -13 = 0
-12 + -7t + 10t2 = 0

Factor a trinomial.
(-4 + -5t)(3 + -2t) = 0

Subproblem 1
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
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 = {-0.8, 1.5}