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

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


Simplifying
0 = 5x3 + 6x2 + x

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

Solving
0 = x + 6x2 + 5x3

Solving for variable 'x'.
Remove the zero:
-1x + -6x2 + -5x3 = x + 6x2 + 5x3 + -1x + -6x2 + -5x3

Reorder the terms:
-1x + -6x2 + -5x3 = x + -1x + 6x2 + -6x2 + 5x3 + -5x3

Combine like terms: x + -1x = 0
-1x + -6x2 + -5x3 = 0 + 6x2 + -6x2 + 5x3 + -5x3
-1x + -6x2 + -5x3 = 6x2 + -6x2 + 5x3 + -5x3

Combine like terms: 6x2 + -6x2 = 0
-1x + -6x2 + -5x3 = 0 + 5x3 + -5x3
-1x + -6x2 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
-1x + -6x2 + -5x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + 6x + 5x2) = 0

Factor a trinomial.
-1x((1 + x)(1 + 5x)) = 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 '(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

Subproblem 3

Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2

Solution

x = {0, -1, -0.2}

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