x^2+7x+45=-9x-3

Solution for x^2+7x+45=-9x-3 equation:

Simplifying
x2 + 7x + 45 = -9x + -3

Reorder the terms:
45 + 7x + x2 = -9x + -3

Reorder the terms:
45 + 7x + x2 = -3 + -9x

Solving
45 + 7x + x2 = -3 + -9x

Solving for variable 'x'.

Reorder the terms:
45 + 3 + 7x + 9x + x2 = -3 + -9x + 3 + 9x

Combine like terms: 45 + 3 = 48
48 + 7x + 9x + x2 = -3 + -9x + 3 + 9x

Combine like terms: 7x + 9x = 16x
48 + 16x + x2 = -3 + -9x + 3 + 9x

Reorder the terms:
48 + 16x + x2 = -3 + 3 + -9x + 9x

Combine like terms: -3 + 3 = 0
48 + 16x + x2 = 0 + -9x + 9x
48 + 16x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
48 + 16x + x2 = 0

Factor a trinomial.
(12 + x)(4 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
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 = {-12, -4}