x^2+5x+1=2x+5

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


Simplifying
x2 + 5x + 1 = 2x + 5

Reorder the terms:
1 + 5x + x2 = 2x + 5

Reorder the terms:
1 + 5x + x2 = 5 + 2x

Solving
1 + 5x + x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -5 + 5x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: 1 + -5 = -4
-4 + 5x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: 5x + -2x = 3x
-4 + 3x + x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-4 + 3x + x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-4 + 3x + x2 = 0 + 2x + -2x
-4 + 3x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + 3x + x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1}

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