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Simplifying -6x(9x2 + -3x + 7) = 0 Reorder the terms: -6x(7 + -3x + 9x2) = 0 (7 * -6x + -3x * -6x + 9x2 * -6x) = 0 (-42x + 18x2 + -54x3) = 0 Solving -42x + 18x2 + -54x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-7 + 3x + -9x2) = 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 '(-7 + 3x + -9x2)' equal to zero and attempt to solve: Simplifying -7 + 3x + -9x2 = 0 Solving -7 + 3x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.7777777778 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -0.3333333333x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -0.3333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + -0.7777777778 -0.3333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -0.3333333333x + x2 = -0.7777777778 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -0.7777777778 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -0.7777777778 + 0.02777777779 Combine like terms: -0.7777777778 + 0.02777777779 = -0.75000000001 0.02777777779 + -0.3333333333x + x2 = -0.75000000001 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.75000000001 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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