f(0)=2X^2+6X-8

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Solution for f(0)=2X^2+6X-8 equation: 


Simplifying
f(0) = 2X2 + 6X + -8

Reorder the terms for easier multiplication:
0f = 2X2 + 6X + -8

Anything times zero is zero.
0f = 2X2 + 6X + -8

Reorder the terms:
0 = -8 + 6X + 2X2

Solving
0 = -8 + 6X + 2X2

Solving for variable 'X'.

Combine like terms: 0 + 8 = 8
8 + -6X + -2X2 = -8 + 6X + 2X2 + 8 + -6X + -2X2

Reorder the terms:
8 + -6X + -2X2 = -8 + 8 + 6X + -6X + 2X2 + -2X2

Combine like terms: -8 + 8 = 0
8 + -6X + -2X2 = 0 + 6X + -6X + 2X2 + -2X2
8 + -6X + -2X2 = 6X + -6X + 2X2 + -2X2

Combine like terms: 6X + -6X = 0
8 + -6X + -2X2 = 0 + 2X2 + -2X2
8 + -6X + -2X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
8 + -6X + -2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -3X + -1X2) = 0

Factor a trinomial.
2((1 + -1X)(4 + X)) = 0

Ignore the factor 2.

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 '(4 + X)' equal to zero and attempt to solve:

Simplifying
4 + X = 0

Solving
4 + X = 0

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

Add '-4' to each side of the equation.
4 + -4 + X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + X = 0 + -4
X = 0 + -4

Combine like terms: 0 + -4 = -4
X = -4

Simplifying
X = -4
Solution
X = {1, -4}

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