f(0)=x^2+5x-14

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Solution for f(0)=x^2+5x-14 equation: 


Simplifying
f(0) = x2 + 5x + -14

Reorder the terms for easier multiplication:
0f = x2 + 5x + -14

Anything times zero is zero.
0f = x2 + 5x + -14

Reorder the terms:
0 = -14 + 5x + x2

Solving
0 = -14 + 5x + x2

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
14 + -5x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
14 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
14 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
14 + -5x + -1x2 = 0 + x2 + -1x2
14 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -5x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(7 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {2, -7}

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