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Simplifying -3x(2x2 + -4x + 9) = 0 Reorder the terms: -3x(9 + -4x + 2x2) = 0 (9 * -3x + -4x * -3x + 2x2 * -3x) = 0 (-27x + 12x2 + -6x3) = 0 Solving -27x + 12x2 + -6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-9 + 4x + -2x2) = 0 Ignore the factor 3.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 '(-9 + 4x + -2x2)' equal to zero and attempt to solve: Simplifying -9 + 4x + -2x2 = 0 Solving -9 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4.5 + -2x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -2x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -2x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -2x + x2 = 0 + -4.5 -2x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -2x + x2 = -4.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -4.5 + 1 Reorder the terms: 1 + -2x + x2 = -4.5 + 1 Combine like terms: -4.5 + 1 = -3.5 1 + -2x + x2 = -3.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -3.5 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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