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Simplifying 4x(2x^{2}+ -6x + -5) = 0 Reorder the terms: 4x(-5 + -6x + 2x^{2}) = 0 (-5 * 4x + -6x * 4x + 2x^{2}* 4x) = 0 (-20x + -24x^{2}+ 8x^{3}) = 0 Solving -20x + -24x^{2}+ 8x^{3}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-5 + -6x + 2x^{2}) = 0 Ignore the factor 4.## 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 = 0## Subproblem 2

Set the factor '(-5 + -6x + 2x^{2})' equal to zero and attempt to solve: Simplifying -5 + -6x + 2x^{2}= 0 Solving -5 + -6x + 2x^{2}= 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3x + x^{2}= 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3x + 2.5 + x^{2}= 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3x + x^{2}= 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3x + x^{2}= 0 + 2.5 -3x + x^{2}= 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3x + x^{2}= 2.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x^{2}= 2.5 + 2.25 Reorder the terms: 2.25 + -3x + x^{2}= 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3x + x^{2}= 4.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -1.5) equal to 2.179449472 and -2.179449472.## Subproblem 1

x + -1.5 = 2.179449472 Simplifying x + -1.5 = 2.179449472 Reorder the terms: -1.5 + x = 2.179449472 Solving -1.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.179449472 + 1.5 x = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 x = 3.679449472 Simplifying x = 3.679449472## Subproblem 2

x + -1.5 = -2.179449472 Simplifying x + -1.5 = -2.179449472 Reorder the terms: -1.5 + x = -2.179449472 Solving -1.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.179449472 + 1.5 x = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 x = -0.679449472 Simplifying x = -0.679449472## Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.679449472, -0.679449472}## Solution

x = {0, 3.679449472, -0.679449472}

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