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

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


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

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

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

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

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

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

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

Solving
3x + 2x2 = -2x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, -2.5}

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