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Simplifying 20x3 + -12x2 + 6x = 0 Reorder the terms: 6x + -12x2 + 20x3 = 0 Solving 6x + -12x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -6x + 10x2) = 0 Ignore the factor 2.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 = 0Subproblem 2
Set the factor '(3 + -6x + 10x2)' equal to zero and attempt to solve: Simplifying 3 + -6x + 10x2 = 0 Solving 3 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -0.6x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + -0.6x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -0.6x + x2 = 0.0 + -0.3 -0.6x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 -0.6x + x2 = -0.3 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 = -0.3 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -0.3 + 0.09 Combine like terms: -0.3 + 0.09 = -0.21 0.09 + -0.6x + x2 = -0.21 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -0.21 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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