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Simplifying -2x(3x2 + -4x + 6) = 0 Reorder the terms: -2x(6 + -4x + 3x2) = 0 (6 * -2x + -4x * -2x + 3x2 * -2x) = 0 (-12x + 8x2 + -6x3) = 0 Solving -12x + 8x2 + -6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-6 + 4x + -3x2) = 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 '(-6 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + -3x2 = 0 Solving -6 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.333333333x + x2 = 0 + -2 -1.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.333333333x + x2 = -2 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -2 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -2 + 0.4444444442 Combine like terms: -2 + 0.4444444442 = -1.5555555558 0.4444444442 + -1.333333333x + x2 = -1.5555555558 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -1.5555555558 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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