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

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


Simplifying
f(0) = -1x2 + 3x + -2

Reorder the terms for easier multiplication:
0f = -1x2 + 3x + -2

Anything times zero is zero.
0f = -1x2 + 3x + -2

Reorder the terms:
0 = -2 + 3x + -1x2

Solving
0 = -2 + 3x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -3x + x2 = -2 + 3x + -1x2 + 2 + -3x + x2

Reorder the terms:
2 + -3x + x2 = -2 + 2 + 3x + -3x + -1x2 + x2

Combine like terms: -2 + 2 = 0
2 + -3x + x2 = 0 + 3x + -3x + -1x2 + x2
2 + -3x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
2 + -3x + x2 = 0 + -1x2 + x2
2 + -3x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2 + -3x + x2 = 0

Factor a trinomial.
(1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

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