t+15=t(t-1)

Solution for t+15=t(t-1) equation:

Simplifying
t + 15 = t(t + -1)

Reorder the terms:
15 + t = t(t + -1)

Reorder the terms:
15 + t = t(-1 + t)
15 + t = (-1 * t + t * t)
15 + t = (-1t + t2)

Solving
15 + t = -1t + t2

Solving for variable 't'.

Combine like terms: t + t = 2t
15 + 2t + -1t2 = -1t + t2 + t + -1t2

Reorder the terms:
15 + 2t + -1t2 = -1t + t + t2 + -1t2

Combine like terms: -1t + t = 0
15 + 2t + -1t2 = 0 + t2 + -1t2
15 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
15 + 2t + -1t2 = 0

Factor a trinomial.
(5 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {5, -3}