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Simplifying (5r + -2)(r + -5) = 0 Reorder the terms: (-2 + 5r)(r + -5) = 0 Reorder the terms: (-2 + 5r)(-5 + r) = 0 Multiply (-2 + 5r) * (-5 + r) (-2(-5 + r) + 5r * (-5 + r)) = 0 ((-5 * -2 + r * -2) + 5r * (-5 + r)) = 0 ((10 + -2r) + 5r * (-5 + r)) = 0 (10 + -2r + (-5 * 5r + r * 5r)) = 0 (10 + -2r + (-25r + 5r2)) = 0 Combine like terms: -2r + -25r = -27r (10 + -27r + 5r2) = 0 Solving 10 + -27r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (2 + -5r)(5 + -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 '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Solution
r = {0.4, 5}
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