3u+18u^2-14u^3=0

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Solution for 3u+18u^2-14u^3=0 equation:


Simplifying
3u + 18u2 + -14u3 = 0

Solving
3u + 18u2 + -14u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(3 + 18u + -14u2) = 0

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 '(3 + 18u + -14u2)' equal to zero and attempt to solve: Simplifying 3 + 18u + -14u2 = 0 Solving 3 + 18u + -14u2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.2142857143 + -1.285714286u + u2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -1.285714286u + 0.2142857143 + u2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -1.285714286u + u2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -1.285714286u + u2 = 0 + 0.2142857143 -1.285714286u + u2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -1.285714286u + u2 = 0.2142857143 The u term is -1.285714286u. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286u + 0.4132653063 + u2 = 0.2142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286u + u2 = 0.2142857143 + 0.4132653063 Combine like terms: 0.2142857143 + 0.4132653063 = 0.6275510206 0.4132653063 + -1.285714286u + u2 = 0.6275510206 Factor a perfect square on the left side: (u + -0.642857143)(u + -0.642857143) = 0.6275510206 Calculate the square root of the right side: 0.792181179 Break this problem into two subproblems by setting (u + -0.642857143) equal to 0.792181179 and -0.792181179.

Subproblem 1

u + -0.642857143 = 0.792181179 Simplifying u + -0.642857143 = 0.792181179 Reorder the terms: -0.642857143 + u = 0.792181179 Solving -0.642857143 + u = 0.792181179 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + u = 0.792181179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + u = 0.792181179 + 0.642857143 u = 0.792181179 + 0.642857143 Combine like terms: 0.792181179 + 0.642857143 = 1.435038322 u = 1.435038322 Simplifying u = 1.435038322

Subproblem 2

u + -0.642857143 = -0.792181179 Simplifying u + -0.642857143 = -0.792181179 Reorder the terms: -0.642857143 + u = -0.792181179 Solving -0.642857143 + u = -0.792181179 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + u = -0.792181179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + u = -0.792181179 + 0.642857143 u = -0.792181179 + 0.642857143 Combine like terms: -0.792181179 + 0.642857143 = -0.149324036 u = -0.149324036 Simplifying u = -0.149324036

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.435038322, -0.149324036}

Solution

u = {0, 1.435038322, -0.149324036}

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