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Simplifying 3x(5 + -1x)(4x + 7) = 0 Reorder the terms: 3x(5 + -1x)(7 + 4x) = 0 Multiply (5 + -1x) * (7 + 4x) 3x(5(7 + 4x) + -1x * (7 + 4x)) = 0 3x((7 * 5 + 4x * 5) + -1x * (7 + 4x)) = 0 3x((35 + 20x) + -1x * (7 + 4x)) = 0 3x(35 + 20x + (7 * -1x + 4x * -1x)) = 0 3x(35 + 20x + (-7x + -4x2)) = 0 Combine like terms: 20x + -7x = 13x 3x(35 + 13x + -4x2) = 0 (35 * 3x + 13x * 3x + -4x2 * 3x) = 0 (105x + 39x2 + -12x3) = 0 Solving 105x + 39x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(35 + 13x + -4x2) = 0 Factor a trinomial. 3x((5 + -1x)(7 + 4x)) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 3
Set the factor '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Solution
x = {0, 5, -1.75}
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