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Simplifying (5r + -2)(r + 4) = 0 Reorder the terms: (-2 + 5r)(r + 4) = 0 Reorder the terms: (-2 + 5r)(4 + r) = 0 Multiply (-2 + 5r) * (4 + r) (-2(4 + r) + 5r * (4 + r)) = 0 ((4 * -2 + r * -2) + 5r * (4 + r)) = 0 ((-8 + -2r) + 5r * (4 + r)) = 0 (-8 + -2r + (4 * 5r + r * 5r)) = 0 (-8 + -2r + (20r + 5r2)) = 0 Combine like terms: -2r + 20r = 18r (-8 + 18r + 5r2) = 0 Solving -8 + 18r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -1r)(2 + -5r) = 0Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 2
Set the factor '(2 + -5r)' equal to zero and attempt to solve: Simplifying 2 + -5r = 0 Solving 2 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5r = 0 + -2 -5r = 0 + -2 Combine like terms: 0 + -2 = -2 -5r = -2 Divide each side by '-5'. r = 0.4 Simplifying r = 0.4Solution
r = {-4, 0.4}
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