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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 = -22r (8 + -22r + 5r2) = 0 Solving 8 + -22r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (2 + -5r)(4 + -1r) = 0Subproblem 1
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 = 0.4Subproblem 2
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 = 4Solution
r = {0.4, 4}
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