f(0)=-2x^2-17x+30

Solution for f(0)=-2x^2-17x+30 equation:

Simplifying
f(0) = -2x2 + -17x + 30

Reorder the terms for easier multiplication:
0f = -2x2 + -17x + 30

Anything times zero is zero.
0f = -2x2 + -17x + 30

Reorder the terms:
0 = 30 + -17x + -2x2

Solving
0 = 30 + -17x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + -30 = -30
-30 + 17x + 2x2 = 30 + -17x + -2x2 + -30 + 17x + 2x2

Reorder the terms:
-30 + 17x + 2x2 = 30 + -30 + -17x + 17x + -2x2 + 2x2

Combine like terms: 30 + -30 = 0
-30 + 17x + 2x2 = 0 + -17x + 17x + -2x2 + 2x2
-30 + 17x + 2x2 = -17x + 17x + -2x2 + 2x2

Combine like terms: -17x + 17x = 0
-30 + 17x + 2x2 = 0 + -2x2 + 2x2
-30 + 17x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-30 + 17x + 2x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-10, 1.5}