0=5x^3+3x^2+6x

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Solution for 0=5x^3+3x^2+6x equation:


Simplifying
0 = 5x3 + 3x2 + 6x

Reorder the terms:
0 = 6x + 3x2 + 5x3

Solving
0 = 6x + 3x2 + 5x3

Solving for variable 'x'.
Remove the zero:
-6x + -3x2 + -5x3 = 6x + 3x2 + 5x3 + -6x + -3x2 + -5x3

Reorder the terms:
-6x + -3x2 + -5x3 = 6x + -6x + 3x2 + -3x2 + 5x3 + -5x3

Combine like terms: 6x + -6x = 0
-6x + -3x2 + -5x3 = 0 + 3x2 + -3x2 + 5x3 + -5x3
-6x + -3x2 + -5x3 = 3x2 + -3x2 + 5x3 + -5x3

Combine like terms: 3x2 + -3x2 = 0
-6x + -3x2 + -5x3 = 0 + 5x3 + -5x3
-6x + -3x2 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
-6x + -3x2 + -5x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(6 + 3x + 5x2) = 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 '(6 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + 5x2 = 0 Solving 6 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 0.6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 0.6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 0.6x + x2 = 0 + -1.2 0.6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 0.6x + x2 = -1.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -1.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -1.2 + 0.09 Combine like terms: -1.2 + 0.09 = -1.11 0.09 + 0.6x + x2 = -1.11 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -1.11 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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