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Simplifying (3x + 1)(2x)(4) = 240 Reorder the terms: (1 + 3x)(2x)(4) = 240 Remove parenthesis around (2x) (1 + 3x) * 2x(4) = 240 Reorder the terms for easier multiplication: 2 * 4x(1 + 3x) = 240 Multiply 2 * 4 8x(1 + 3x) = 240 (1 * 8x + 3x * 8x) = 240 (8x + 24x2) = 240 Solving 8x + 24x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 8x + 24x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 8x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-30 + x + 3x2) = 0 Factor a trinomial. 8((-10 + -3x)(3 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3.333333333, 3}
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