3x^2+3x+1=2x+1

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


Simplifying
3x2 + 3x + 1 = 2x + 1

Reorder the terms:
1 + 3x + 3x2 = 2x + 1

Reorder the terms:
1 + 3x + 3x2 = 1 + 2x

Add '-1' to each side of the equation.
1 + 3x + -1 + 3x2 = 1 + -1 + 2x

Reorder the terms:
1 + -1 + 3x + 3x2 = 1 + -1 + 2x

Combine like terms: 1 + -1 = 0
0 + 3x + 3x2 = 1 + -1 + 2x
3x + 3x2 = 1 + -1 + 2x

Combine like terms: 1 + -1 = 0
3x + 3x2 = 0 + 2x
3x + 3x2 = 2x

Solving
3x + 3x2 = 2x

Solving for variable 'x'.

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

Combine like terms: 3x + -2x = 1x
1x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
1x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 3x) = 0


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 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0, -0.3333333333}

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