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Simplifying 12x3 + 15x2 + 6x = 0 Reorder the terms: 6x + 15x2 + 12x3 = 0 Solving 6x + 15x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(2 + 5x + 4x2) = 0 Ignore the factor 3.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 '(2 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + 4x2 = 0 Solving 2 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.25x + x2 = 0 + -0.5 1.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.25x + x2 = -0.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.5 + 0.390625 Combine like terms: -0.5 + 0.390625 = -0.109375 0.390625 + 1.25x + x2 = -0.109375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -0.109375 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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