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Simplifying -2x2(3x2 + -2x + 3) = 0 Reorder the terms: -2x2(3 + -2x + 3x2) = 0 (3 * -2x2 + -2x * -2x2 + 3x2 * -2x2) = 0 (-6x2 + 4x3 + -6x4) = 0 Solving -6x2 + 4x3 + -6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-3 + 2x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3 + 2x + -3x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + -3x2 = 0 Solving -3 + 2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.6666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.6666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.6666666667x + x2 = 0 + -1 -0.6666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.6666666667x + x2 = -1 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -1 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + -0.6666666667x + x2 = -0.8888888888 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.8888888888 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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