f(0)=-x^2+4x-3

Solution for f(0)=-x^2+4x-3 equation:

Simplifying
f(0) = -1x2 + 4x + -3

Reorder the terms for easier multiplication:
0f = -1x2 + 4x + -3

Anything times zero is zero.
0f = -1x2 + 4x + -3

Reorder the terms:
0 = -3 + 4x + -1x2

Solving
0 = -3 + 4x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -4x + x2 = -3 + 4x + -1x2 + 3 + -4x + x2

Reorder the terms:
3 + -4x + x2 = -3 + 3 + 4x + -4x + -1x2 + x2

Combine like terms: -3 + 3 = 0
3 + -4x + x2 = 0 + 4x + -4x + -1x2 + x2
3 + -4x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
3 + -4x + x2 = 0 + -1x2 + x2
3 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3 + -4x + x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
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
Solution
x = {1, 3}