x^2+3x+1=7x+22

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Solution for x^2+3x+1=7x+22 equation: 


Simplifying
x2 + 3x + 1 = 7x + 22

Reorder the terms:
1 + 3x + x2 = 7x + 22

Reorder the terms:
1 + 3x + x2 = 22 + 7x

Solving
1 + 3x + x2 = 22 + 7x

Solving for variable 'x'.

Reorder the terms:
1 + -22 + 3x + -7x + x2 = 22 + 7x + -22 + -7x

Combine like terms: 1 + -22 = -21
-21 + 3x + -7x + x2 = 22 + 7x + -22 + -7x

Combine like terms: 3x + -7x = -4x
-21 + -4x + x2 = 22 + 7x + -22 + -7x

Reorder the terms:
-21 + -4x + x2 = 22 + -22 + 7x + -7x

Combine like terms: 22 + -22 = 0
-21 + -4x + x2 = 0 + 7x + -7x
-21 + -4x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-21 + -4x + x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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