f(0)=4x^2-8x+4

Solution for f(0)=4x^2-8x+4 equation:

Simplifying
f(0) = 4x2 + -8x + 4

Reorder the terms for easier multiplication:
0f = 4x2 + -8x + 4

Anything times zero is zero.
0f = 4x2 + -8x + 4

Reorder the terms:
0 = 4 + -8x + 4x2

Solving
0 = 4 + -8x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Reorder the terms:
-4 + 8x + -4x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
-4 + 8x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
-4 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
-4 + 8x + -4x2 = 0 + 4x2 + -4x2
-4 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 2x + -1x2) = 0

Factor a trinomial.
4((-1 + x)(1 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

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