x^2+5x+1=7

Solution for x^2+5x+1=7 equation:

Simplifying
x2 + 5x + 1 = 7

Reorder the terms:
1 + 5x + x2 = 7

Solving
1 + 5x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 5x + x2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 5x + x2 = 7 + -7

Combine like terms: 7 + -7 = 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}