y^2+6y-27=0

Solution for y^2+6y-27=0 equation:

Simplifying
y2 + 6y + -27 = 0

Reorder the terms:
-27 + 6y + y2 = 0

Solving
-27 + 6y + y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

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

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

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

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

Simplifying
y = -9
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

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