t(13t+3)=10

Solution for t(13t+3)=10 equation:

Simplifying
t(13t + 3) = 10

Reorder the terms:
t(3 + 13t) = 10
(3 * t + 13t * t) = 10
(3t + 13t2) = 10

Solving
3t + 13t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + 3t + 13t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 3t + 13t2 = 0

Factor a trinomial.
(-1 + -1t)(10 + -13t) = 0

Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve:

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 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 + -1t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t = 0 + 1
-1t = 0 + 1

Combine like terms: 0 + 1 = 1
-1t = 1

Divide each side by '-1'.
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(10 + -13t)' equal to zero and attempt to solve:

Simplifying
10 + -13t = 0

Solving
10 + -13t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -13t = 0 + -10

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

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

Divide each side by '-13'.
t = 0.7692307692

Simplifying
t = 0.7692307692
Solution
t = {-1, 0.7692307692}