f(0)=2x^2+6x-6

Solution for f(0)=2x^2+6x-6 equation:

Simplifying
f(0) = 2x2 + 6x + -6

Reorder the terms for easier multiplication:
0f = 2x2 + 6x + -6

Anything times zero is zero.
0f = 2x2 + 6x + -6

Reorder the terms:
0 = -6 + 6x + 2x2

Solving
0 = -6 + 6x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -6x + -2x2 = -6 + 6x + 2x2 + 6 + -6x + -2x2

Reorder the terms:
6 + -6x + -2x2 = -6 + 6 + 6x + -6x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2
6 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
6 + -6x + -2x2 = 0 + 2x2 + -2x2
6 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -3x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -3x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + -1x2 = 0

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 3x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3x + 3 + x2 = 0 + 3

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

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

Combine like terms: 0 + 3 = 3
3x + x2 = 3

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 3 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3x + x2 = 5.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 1.5 = 2.291287847

Simplifying
x + 1.5 = 2.291287847

Reorder the terms:
1.5 + x = 2.291287847

Solving
1.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.291287847 + -1.5
x = 2.291287847 + -1.5

Combine like terms: 2.291287847 + -1.5 = 0.791287847
x = 0.791287847

Simplifying
x = 0.791287847

Subproblem 2
x + 1.5 = -2.291287847

Simplifying
x + 1.5 = -2.291287847

Reorder the terms:
1.5 + x = -2.291287847

Solving
1.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.291287847 + -1.5
x = -2.291287847 + -1.5

Combine like terms: -2.291287847 + -1.5 = -3.791287847
x = -3.791287847

Simplifying
x = -3.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.791287847, -3.791287847}
Solution
x = {0.791287847, -3.791287847}