x^2+12x+16=7x+22

Solution for x^2+12x+16=7x+22 equation:

Simplifying
x2 + 12x + 16 = 7x + 22

Reorder the terms:
16 + 12x + x2 = 7x + 22

Reorder the terms:
16 + 12x + x2 = 22 + 7x

Solving
16 + 12x + x2 = 22 + 7x

Solving for variable 'x'.

Reorder the terms:
16 + -22 + 12x + -7x + x2 = 22 + 7x + -22 + -7x

Combine like terms: 16 + -22 = -6
-6 + 12x + -7x + x2 = 22 + 7x + -22 + -7x

Combine like terms: 12x + -7x = 5x
-6 + 5x + x2 = 22 + 7x + -22 + -7x

Reorder the terms:
-6 + 5x + x2 = 22 + -22 + 7x + -7x

Combine like terms: 22 + -22 = 0
-6 + 5x + x2 = 0 + 7x + -7x
-6 + 5x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 1}