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Simplifying (6x3 + 2x2 + 3x) + -1(3x3 + -2x2 + -3x) = 0 Reorder the terms: (3x + 2x2 + 6x3) + -1(3x3 + -2x2 + -3x) = 0 Remove parenthesis around (3x + 2x2 + 6x3) 3x + 2x2 + 6x3 + -1(3x3 + -2x2 + -3x) = 0 Reorder the terms: 3x + 2x2 + 6x3 + -1(-3x + -2x2 + 3x3) = 0 3x + 2x2 + 6x3 + (-3x * -1 + -2x2 * -1 + 3x3 * -1) = 0 3x + 2x2 + 6x3 + (3x + 2x2 + -3x3) = 0 Reorder the terms: 3x + 3x + 2x2 + 2x2 + 6x3 + -3x3 = 0 Combine like terms: 3x + 3x = 6x 6x + 2x2 + 2x2 + 6x3 + -3x3 = 0 Combine like terms: 2x2 + 2x2 = 4x2 6x + 4x2 + 6x3 + -3x3 = 0 Combine like terms: 6x3 + -3x3 = 3x3 6x + 4x2 + 3x3 = 0 Solving 6x + 4x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + 4x + 3x2) = 0Subproblem 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 '(6 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + 4x + 3x2 = 0 Solving 6 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.333333333x + x2 = 0 + -2 1.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.333333333x + x2 = -2 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -2 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -2 + 0.4444444442 Combine like terms: -2 + 0.4444444442 = -1.5555555558 0.4444444442 + 1.333333333x + x2 = -1.5555555558 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.5555555558 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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