t(t+4)=60

Solution for t(t+4)=60 equation:

Simplifying
t(t + 4) = 60

Reorder the terms:
t(4 + t) = 60
(4 * t + t * t) = 60
(4t + t2) = 60

Solving
4t + t2 = 60

Solving for variable 't'.

Reorder the terms:
-60 + 4t + t2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 4t + t2 = 0

Factor a trinomial.
(-10 + -1t)(6 + -1t) = 0

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

Simplifying
-10 + -1t = 0

Solving
-10 + -1t = 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 + -1t = 0 + 10

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

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

Divide each side by '-1'.
t = -10

Simplifying
t = -10
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-10, 6}