t^2-24t+144=900

Solution for t^2-24t+144=900 equation:

Simplifying
t2 + -24t + 144 = 900

Reorder the terms:
144 + -24t + t2 = 900

Solving
144 + -24t + t2 = 900

Solving for variable 't'.

Reorder the terms:
144 + -900 + -24t + t2 = 900 + -900

Combine like terms: 144 + -900 = -756
-756 + -24t + t2 = 900 + -900

Combine like terms: 900 + -900 = 0
-756 + -24t + t2 = 0

Factor a trinomial.
(-18 + -1t)(42 + -1t) = 0

Subproblem 1
Set the factor '(-18 + -1t)' equal to zero and attempt to solve:

Simplifying
-18 + -1t = 0

Solving
-18 + -1t = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1t = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1t = 0 + 18
-1t = 0 + 18

Combine like terms: 0 + 18 = 18
-1t = 18

Divide each side by '-1'.
t = -18

Simplifying
t = -18
Subproblem 2
Set the factor '(42 + -1t)' equal to zero and attempt to solve:

Simplifying
42 + -1t = 0

Solving
42 + -1t = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1t = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1t = 0 + -42
-1t = 0 + -42

Combine like terms: 0 + -42 = -42
-1t = -42

Divide each side by '-1'.
t = 42

Simplifying
t = 42
Solution
t = {-18, 42}