f(0)=-x^2+6x+27

Solution for f(0)=-x^2+6x+27 equation:

Simplifying
f(0) = -1x2 + 6x + 27

Reorder the terms for easier multiplication:
0f = -1x2 + 6x + 27

Anything times zero is zero.
0f = -1x2 + 6x + 27

Reorder the terms:
0 = 27 + 6x + -1x2

Solving
0 = 27 + 6x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -27 = -27
-27 + -6x + x2 = 27 + 6x + -1x2 + -27 + -6x + x2

Reorder the terms:
-27 + -6x + x2 = 27 + -27 + 6x + -6x + -1x2 + x2

Combine like terms: 27 + -27 = 0
-27 + -6x + x2 = 0 + 6x + -6x + -1x2 + x2
-27 + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
-27 + -6x + x2 = 0 + -1x2 + x2
-27 + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-27 + -6x + x2 = 0

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

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

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

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

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

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

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

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

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

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