0=x^2+14x+45

Solution for 0=x^2+14x+45 equation:

Simplifying
0 = x2 + 14x + 45

Reorder the terms:
0 = 45 + 14x + x2

Solving
0 = 45 + 14x + x2

Solving for variable 'x'.

Combine like terms: 0 + -45 = -45
-45 + -14x + -1x2 = 45 + 14x + x2 + -45 + -14x + -1x2

Reorder the terms:
-45 + -14x + -1x2 = 45 + -45 + 14x + -14x + x2 + -1x2

Combine like terms: 45 + -45 = 0
-45 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-45 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-45 + -14x + -1x2 = 0 + x2 + -1x2
-45 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 14x + x2) = 0

Factor a trinomial.
-1((9 + x)(5 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-9, -5}