27=t(t-6)

Solution for 27=t(t-6) equation:

Simplifying
27 = t(t + -6)

Reorder the terms:
27 = t(-6 + t)
27 = (-6 * t + t * t)
27 = (-6t + t2)

Solving
27 = -6t + t2

Solving for variable 't'.

Reorder the terms:
27 + 6t + -1t2 = -6t + 6t + t2 + -1t2

Combine like terms: -6t + 6t = 0
27 + 6t + -1t2 = 0 + t2 + -1t2
27 + 6t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
27 + 6t + -1t2 = 0

Factor a trinomial.
(9 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {9, -3}