5x^2+6x+1=x^2+2x+1

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Solution for 5x^2+6x+1=x^2+2x+1 equation: 


Simplifying
5x2 + 6x + 1 = x2 + 2x + 1

Reorder the terms:
1 + 6x + 5x2 = x2 + 2x + 1

Reorder the terms:
1 + 6x + 5x2 = 1 + 2x + x2

Add '-1' to each side of the equation.
1 + 6x + -1 + 5x2 = 1 + 2x + -1 + x2

Reorder the terms:
1 + -1 + 6x + 5x2 = 1 + 2x + -1 + x2

Combine like terms: 1 + -1 = 0
0 + 6x + 5x2 = 1 + 2x + -1 + x2
6x + 5x2 = 1 + 2x + -1 + x2

Reorder the terms:
6x + 5x2 = 1 + -1 + 2x + x2

Combine like terms: 1 + -1 = 0
6x + 5x2 = 0 + 2x + x2
6x + 5x2 = 2x + x2

Solving
6x + 5x2 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
6x + -2x + 5x2 + -1x2 = 2x + x2 + -2x + -1x2

Combine like terms: 6x + -2x = 4x
4x + 5x2 + -1x2 = 2x + x2 + -2x + -1x2

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

Reorder the terms:
4x + 4x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
4x + 4x2 = 0 + x2 + -1x2
4x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, -1}

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