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

Solution for 25(t-1)=t(t+15) equation:

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

Reorder the terms:
25(-1 + t) = t(t + 15)
(-1 * 25 + t * 25) = t(t + 15)
(-25 + 25t) = t(t + 15)

Reorder the terms:
-25 + 25t = t(15 + t)
-25 + 25t = (15 * t + t * t)
-25 + 25t = (15t + t2)

Solving
-25 + 25t = 15t + t2

Solving for variable 't'.

Combine like terms: 25t + -15t = 10t
-25 + 10t + -1t2 = 15t + t2 + -15t + -1t2

Reorder the terms:
-25 + 10t + -1t2 = 15t + -15t + t2 + -1t2

Combine like terms: 15t + -15t = 0
-25 + 10t + -1t2 = 0 + t2 + -1t2
-25 + 10t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-25 + 10t + -1t2 = 0

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

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

Simplifying
-5 + t = 0

Solving
-5 + t = 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 + t = 0 + 5

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

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

Simplifying
t = 5
Subproblem 2
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
Solution
t = {5, 5}