9u^3+6u^2-18u=

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Solution for 9u^3+6u^2-18u= equation:


Simplifying
9u3 + 6u2 + -18u = 0

Reorder the terms:
-18u + 6u2 + 9u3 = 0

Solving
-18u + 6u2 + 9u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u'.
3u(-6 + 2u + 3u2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0

Subproblem 2

Set the factor '(-6 + 2u + 3u2)' equal to zero and attempt to solve: Simplifying -6 + 2u + 3u2 = 0 Solving -6 + 2u + 3u2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 0.6666666667u + u2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6666666667u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6666666667u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6666666667u + u2 = 0 + 2 0.6666666667u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6666666667u + u2 = 2 The u term is 0.6666666667u. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667u + 0.1111111112 + u2 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667u + u2 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + 0.6666666667u + u2 = 2.1111111112 Factor a perfect square on the left side: (u + 0.3333333334)(u + 0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (u + 0.3333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1

u + 0.3333333334 = 1.452966315 Simplifying u + 0.3333333334 = 1.452966315 Reorder the terms: 0.3333333334 + u = 1.452966315 Solving 0.3333333334 + u = 1.452966315 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + u = 1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + u = 1.452966315 + -0.3333333334 u = 1.452966315 + -0.3333333334 Combine like terms: 1.452966315 + -0.3333333334 = 1.1196329816 u = 1.1196329816 Simplifying u = 1.1196329816

Subproblem 2

u + 0.3333333334 = -1.452966315 Simplifying u + 0.3333333334 = -1.452966315 Reorder the terms: 0.3333333334 + u = -1.452966315 Solving 0.3333333334 + u = -1.452966315 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + u = -1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + u = -1.452966315 + -0.3333333334 u = -1.452966315 + -0.3333333334 Combine like terms: -1.452966315 + -0.3333333334 = -1.7862996484 u = -1.7862996484 Simplifying u = -1.7862996484

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.1196329816, -1.7862996484}

Solution

u = {0, 1.1196329816, -1.7862996484}

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