0=x^3+4x^2+3x

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Solution for 0=x^3+4x^2+3x equation:


Simplifying
0 = x3 + 4x2 + 3x

Reorder the terms:
0 = 3x + 4x2 + x3

Solving
0 = 3x + 4x2 + x3

Solving for variable 'x'.
Remove the zero:
-3x + -4x2 + -1x3 = 3x + 4x2 + x3 + -3x + -4x2 + -1x3

Reorder the terms:
-3x + -4x2 + -1x3 = 3x + -3x + 4x2 + -4x2 + x3 + -1x3

Combine like terms: 3x + -3x = 0
-3x + -4x2 + -1x3 = 0 + 4x2 + -4x2 + x3 + -1x3
-3x + -4x2 + -1x3 = 4x2 + -4x2 + x3 + -1x3

Combine like terms: 4x2 + -4x2 = 0
-3x + -4x2 + -1x3 = 0 + x3 + -1x3
-3x + -4x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-3x + -4x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(3 + 4x + x2) = 0

Factor a trinomial.
-1x((3 + x)(1 + x)) = 0

Ignore the factor -1.

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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 3

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, -3, -1}

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