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Simplifying -3x(4x2 + -6x + 12) = 0 Reorder the terms: -3x(12 + -6x + 4x2) = 0 (12 * -3x + -6x * -3x + 4x2 * -3x) = 0 (-36x + 18x2 + -12x3) = 0 Solving -36x + 18x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-6 + 3x + -2x2) = 0 Ignore the factor 6.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 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + -2x2 = 0 Solving -6 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3 + -1.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.5x + x2 = 0 + -3 -1.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.5x + x2 = -3 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -3 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + -1.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -2.4375 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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