27=a(a-6)

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

Simplifying
27 = a(a + -6)

Reorder the terms:
27 = a(-6 + a)
27 = (-6 * a + a * a)
27 = (-6a + a2)

Solving
27 = -6a + a2

Solving for variable 'a'.

Reorder the terms:
27 + 6a + -1a2 = -6a + 6a + a2 + -1a2

Combine like terms: -6a + 6a = 0
27 + 6a + -1a2 = 0 + a2 + -1a2
27 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
27 + 6a + -1a2 = 0

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

Subproblem 1
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1a = 0 + -9

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

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

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

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

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

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