x^2+19x+33=7x+1

Solution for x^2+19x+33=7x+1 equation:

Simplifying
x2 + 19x + 33 = 7x + 1

Reorder the terms:
33 + 19x + x2 = 7x + 1

Reorder the terms:
33 + 19x + x2 = 1 + 7x

Solving
33 + 19x + x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
33 + -1 + 19x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: 33 + -1 = 32
32 + 19x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: 19x + -7x = 12x
32 + 12x + x2 = 1 + 7x + -1 + -7x

Reorder the terms:
32 + 12x + x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
32 + 12x + x2 = 0 + 7x + -7x
32 + 12x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
32 + 12x + x2 = 0

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

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
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 = {-8, -4}