f(0)=x^2+11x+18

Solution for f(0)=x^2+11x+18 equation:

Simplifying
f(0) = x2 + 11x + 18

Reorder the terms for easier multiplication:
0f = x2 + 11x + 18

Anything times zero is zero.
0f = x2 + 11x + 18

Reorder the terms:
0 = 18 + 11x + x2

Solving
0 = 18 + 11x + x2

Solving for variable 'x'.

Combine like terms: 0 + -18 = -18
-18 + -11x + -1x2 = 18 + 11x + x2 + -18 + -11x + -1x2

Reorder the terms:
-18 + -11x + -1x2 = 18 + -18 + 11x + -11x + x2 + -1x2

Combine like terms: 18 + -18 = 0
-18 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2
-18 + -11x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
-18 + -11x + -1x2 = 0 + x2 + -1x2
-18 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 11x + x2) = 0

Factor a trinomial.
-1((9 + x)(2 + x)) = 0

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-9, -2}