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Simplifying 6x2(-3x2 + 8x + -6) = 0 Reorder the terms: 6x2(-6 + 8x + -3x2) = 0 (-6 * 6x2 + 8x * 6x2 + -3x2 * 6x2) = 0 (-36x2 + 48x3 + -18x4) = 0 Solving -36x2 + 48x3 + -18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(-6 + 8x + -3x2) = 0 Ignore the factor 6.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 '(-6 + 8x + -3x2)' equal to zero and attempt to solve: Simplifying -6 + 8x + -3x2 = 0 Solving -6 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.666666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.666666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.666666667x + x2 = 0 + -2 -2.666666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.666666667x + x2 = -2 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -2 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -2 + 1.777777780 Combine like terms: -2 + 1.777777780 = -0.22222222 1.777777780 + -2.666666667x + x2 = -0.22222222 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -0.22222222 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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