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Simplifying 5x(x + -4)(2x + 7) = 0 Reorder the terms: 5x(-4 + x)(2x + 7) = 0 Reorder the terms: 5x(-4 + x)(7 + 2x) = 0 Multiply (-4 + x) * (7 + 2x) 5x(-4(7 + 2x) + x(7 + 2x)) = 0 5x((7 * -4 + 2x * -4) + x(7 + 2x)) = 0 5x((-28 + -8x) + x(7 + 2x)) = 0 5x(-28 + -8x + (7 * x + 2x * x)) = 0 5x(-28 + -8x + (7x + 2x2)) = 0 Combine like terms: -8x + 7x = -1x 5x(-28 + -1x + 2x2) = 0 (-28 * 5x + -1x * 5x + 2x2 * 5x) = 0 (-140x + -5x2 + 10x3) = 0 Solving -140x + -5x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-28 + -1x + 2x2) = 0 Factor a trinomial. 5x((-7 + -2x)(4 + -1x)) = 0 Ignore the factor 5.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 '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, -3.5, 4}
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