=t(t-5)

Solution for =t(t-5) equation:

Simplifying
0 = t(t + -5)

Reorder the terms:
0 = t(-5 + t)
0 = (-5 * t + t * t)
0 = (-5t + t2)

Solving
0 = -5t + t2

Solving for variable 't'.
Remove the zero:
5t + -1t2 = -5t + t2 + 5t + -1t2

Reorder the terms:
5t + -1t2 = -5t + 5t + t2 + -1t2

Combine like terms: -5t + 5t = 0
5t + -1t2 = 0 + t2 + -1t2
5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
5t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(5 + -1t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
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 = {0, 5}