T(T+3)=18

Solution for T(T+3)=18 equation:

Simplifying
T(T + 3) = 18

Reorder the terms:
T(3 + T) = 18
(3 * T + T * T) = 18
(3T + T2) = 18

Solving
3T + T2 = 18

Solving for variable 'T'.

Reorder the terms:
-18 + 3T + T2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 3T + T2 = 0

Factor a trinomial.
(-6 + -1T)(3 + -1T) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1T)' equal to zero and attempt to solve:

Simplifying
3 + -1T = 0

Solving
3 + -1T = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1T = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1T = 0 + -3
-1T = 0 + -3

Combine like terms: 0 + -3 = -3
-1T = -3

Divide each side by '-1'.
T = 3

Simplifying
T = 3
Solution
T = {-6, 3}