t^2+24t=3456

Solution for t^2+24t=3456 equation:

Simplifying
t2 + 24t = 3456

Reorder the terms:
24t + t2 = 3456

Solving
24t + t2 = 3456

Solving for variable 't'.

Reorder the terms:
-3456 + 24t + t2 = 3456 + -3456

Combine like terms: 3456 + -3456 = 0
-3456 + 24t + t2 = 0

Factor a trinomial.
(-72 + -1t)(48 + -1t) = 0

Subproblem 1
Set the factor '(-72 + -1t)' equal to zero and attempt to solve:

Simplifying
-72 + -1t = 0

Solving
-72 + -1t = 0

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

Add '72' to each side of the equation.
-72 + 72 + -1t = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -1t = 0 + 72
-1t = 0 + 72

Combine like terms: 0 + 72 = 72
-1t = 72

Divide each side by '-1'.
t = -72

Simplifying
t = -72
Subproblem 2
Set the factor '(48 + -1t)' equal to zero and attempt to solve:

Simplifying
48 + -1t = 0

Solving
48 + -1t = 0

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

Add '-48' to each side of the equation.
48 + -48 + -1t = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -1t = 0 + -48
-1t = 0 + -48

Combine like terms: 0 + -48 = -48
-1t = -48

Divide each side by '-1'.
t = 48

Simplifying
t = 48
Solution
t = {-72, 48}