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Simplifying 5x3 + -6x2 + 12x = 0 Reorder the terms: 12x + -6x2 + 5x3 = 0 Solving 12x + -6x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -6x + 5x2) = 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 '(12 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + -6x + 5x2 = 0 Solving 12 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -1.2x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -1.2x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -1.2x + x2 = 0 + -2.4 -1.2x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -1.2x + x2 = -2.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -2.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -2.4 + 0.36 Combine like terms: -2.4 + 0.36 = -2.04 0.36 + -1.2x + x2 = -2.04 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -2.04 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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