6x(6x^2-18x+2)=0

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Solution for 6x(6x^2-18x+2)=0 equation:


Simplifying
6x(6x2 + -18x + 2) = 0

Reorder the terms:
6x(2 + -18x + 6x2) = 0
(2 * 6x + -18x * 6x + 6x2 * 6x) = 0
(12x + -108x2 + 36x3) = 0

Solving
12x + -108x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(1 + -9x + 3x2) = 0

Ignore the factor 12.

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 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -9x + 3x2 = 0 Solving 1 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -3x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -3x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -3x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.3333333333 -3x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -3x + x2 = -0.3333333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.3333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.3333333333 + 2.25 Combine like terms: -0.3333333333 + 2.25 = 1.9166666667 2.25 + -3x + x2 = 1.9166666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.9166666667 Calculate the square root of the right side: 1.38443731 Break this problem into two subproblems by setting (x + -1.5) equal to 1.38443731 and -1.38443731.

Subproblem 1

x + -1.5 = 1.38443731 Simplifying x + -1.5 = 1.38443731 Reorder the terms: -1.5 + x = 1.38443731 Solving -1.5 + x = 1.38443731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.38443731 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.38443731 + 1.5 x = 1.38443731 + 1.5 Combine like terms: 1.38443731 + 1.5 = 2.88443731 x = 2.88443731 Simplifying x = 2.88443731

Subproblem 2

x + -1.5 = -1.38443731 Simplifying x + -1.5 = -1.38443731 Reorder the terms: -1.5 + x = -1.38443731 Solving -1.5 + x = -1.38443731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.38443731 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.38443731 + 1.5 x = -1.38443731 + 1.5 Combine like terms: -1.38443731 + 1.5 = 0.11556269 x = 0.11556269 Simplifying x = 0.11556269

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.88443731, 0.11556269}

Solution

x = {0, 2.88443731, 0.11556269}

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