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Simplifying 5(x + 2)(x + 4n) = 0 Reorder the terms: 5(2 + x)(x + 4n) = 0 Reorder the terms: 5(2 + x)(4n + x) = 0 Multiply (2 + x) * (4n + x) 5(2(4n + x) + x(4n + x)) = 0 5((4n * 2 + x * 2) + x(4n + x)) = 0 5((8n + 2x) + x(4n + x)) = 0 5(8n + 2x + (4n * x + x * x)) = 0 5(8n + 2x + (4nx + x2)) = 0 Reorder the terms: 5(8n + 4nx + 2x + x2) = 0 5(8n + 4nx + 2x + x2) = 0 (8n * 5 + 4nx * 5 + 2x * 5 + x2 * 5) = 0 (40n + 20nx + 10x + 5x2) = 0 Solving 40n + 20nx + 10x + 5x2 = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10x' to each side of the equation. 40n + 20nx + 10x + -10x + 5x2 = 0 + -10x Combine like terms: 10x + -10x = 0 40n + 20nx + 0 + 5x2 = 0 + -10x 40n + 20nx + 5x2 = 0 + -10x Remove the zero: 40n + 20nx + 5x2 = -10x Add '-5x2' to each side of the equation. 40n + 20nx + 5x2 + -5x2 = -10x + -5x2 Combine like terms: 5x2 + -5x2 = 0 40n + 20nx + 0 = -10x + -5x2 40n + 20nx = -10x + -5x2 Reorder the terms: 40n + 20nx + 10x + 5x2 = -10x + 10x + -5x2 + 5x2 Combine like terms: -10x + 10x = 0 40n + 20nx + 10x + 5x2 = 0 + -5x2 + 5x2 40n + 20nx + 10x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 40n + 20nx + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8n + 4nx + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8n + 4nx + 2x + x2)' equal to zero and attempt to solve: Simplifying 8n + 4nx + 2x + x2 = 0 Solving 8n + 4nx + 2x + x2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-2x' to each side of the equation. 8n + 4nx + 2x + -2x + x2 = 0 + -2x Combine like terms: 2x + -2x = 0 8n + 4nx + 0 + x2 = 0 + -2x 8n + 4nx + x2 = 0 + -2x Remove the zero: 8n + 4nx + x2 = -2x Add '-1x2' to each side of the equation. 8n + 4nx + x2 + -1x2 = -2x + -1x2 Combine like terms: x2 + -1x2 = 0 8n + 4nx + 0 = -2x + -1x2 8n + 4nx = -2x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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