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Simplifying -6x2(-7x2 + x + -3) = 0 Reorder the terms: -6x2(-3 + x + -7x2) = 0 (-3 * -6x2 + x * -6x2 + -7x2 * -6x2) = 0 (18x2 + -6x3 + 42x4) = 0 Solving 18x2 + -6x3 + 42x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(3 + -1x + 7x2) = 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 '(3 + -1x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + 7x2 = 0 Solving 3 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.1428571429x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -0.1428571429x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + -0.4285714286 -0.1428571429x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -0.1428571429x + x2 = -0.4285714286 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = -0.4285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = -0.4285714286 + 0.005102040819 Combine like terms: -0.4285714286 + 0.005102040819 = -0.423469387781 0.005102040819 + -0.1428571429x + x2 = -0.423469387781 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = -0.423469387781 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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