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Simplifying (2x + 4x)(3x2 + 2x) + 16x = 0 Combine like terms: 2x + 4x = 6x (6x)(3x2 + 2x) + 16x = 0 Remove parenthesis around (6x) 6x(3x2 + 2x) + 16x = 0 Reorder the terms: 6x(2x + 3x2) + 16x = 0 (2x * 6x + 3x2 * 6x) + 16x = 0 (12x2 + 18x3) + 16x = 0 Reorder the terms: 16x + 12x2 + 18x3 = 0 Solving 16x + 12x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(8 + 6x + 9x2) = 0 Ignore the factor 2.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 '(8 + 6x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + 6x + 9x2 = 0 Solving 8 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 0.6666666667x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 0.6666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.8888888889 0.6666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 0.6666666667x + x2 = -0.8888888889 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 = -0.8888888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.8888888889 + 0.1111111112 Combine like terms: -0.8888888889 + 0.1111111112 = -0.7777777777 0.1111111112 + 0.6666666667x + x2 = -0.7777777777 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.7777777777 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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