t(t-13)=30

Solution for t(t-13)=30 equation:

Simplifying
t(t + -13) = 30

Reorder the terms:
t(-13 + t) = 30
(-13 * t + t * t) = 30
(-13t + t2) = 30

Solving
-13t + t2 = 30

Solving for variable 't'.

Reorder the terms:
-30 + -13t + t2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -13t + t2 = 0

Factor a trinomial.
(-2 + -1t)(15 + -1t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve:

Simplifying
15 + -1t = 0

Solving
15 + -1t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1t = 0 + -15
-1t = 0 + -15

Combine like terms: 0 + -15 = -15
-1t = -15

Divide each side by '-1'.
t = 15

Simplifying
t = 15
Solution
t = {-2, 15}