4x^2+3x+1=1-x

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Solution for 4x^2+3x+1=1-x equation:


Simplifying
4x2 + 3x + 1 = 1 + -1x

Reorder the terms:
1 + 3x + 4x2 = 1 + -1x

Add '-1' to each side of the equation.
1 + 3x + -1 + 4x2 = 1 + -1 + -1x

Reorder the terms:
1 + -1 + 3x + 4x2 = 1 + -1 + -1x

Combine like terms: 1 + -1 = 0
0 + 3x + 4x2 = 1 + -1 + -1x
3x + 4x2 = 1 + -1 + -1x

Combine like terms: 1 + -1 = 0
3x + 4x2 = 0 + -1x
3x + 4x2 = -1x

Solving
3x + 4x2 = -1x

Solving for variable 'x'.

Reorder the terms:
3x + x + 4x2 = -1x + x

Combine like terms: 3x + x = 4x
4x + 4x2 = -1x + x

Combine like terms: -1x + x = 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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