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Simplifying 2x(5x2 + -4(x + -3)) = 0 Reorder the terms: 2x(5x2 + -4(-3 + x)) = 0 2x(5x2 + (-3 * -4 + x * -4)) = 0 2x(5x2 + (12 + -4x)) = 0 Reorder the terms: 2x(12 + -4x + 5x2) = 0 (12 * 2x + -4x * 2x + 5x2 * 2x) = 0 (24x + -8x2 + 10x3) = 0 Solving 24x + -8x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(12 + -4x + 5x2) = 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 '(12 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + -4x + 5x2 = 0 Solving 12 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -0.8x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -0.8x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -0.8x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -0.8x + x2 = 0 + -2.4 -0.8x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -0.8x + x2 = -2.4 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -2.4 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -2.4 + 0.16 Combine like terms: -2.4 + 0.16 = -2.24 0.16 + -0.8x + x2 = -2.24 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -2.24 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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