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Simplifying (5r + 4)(2r + -5) = 0 Reorder the terms: (4 + 5r)(2r + -5) = 0 Reorder the terms: (4 + 5r)(-5 + 2r) = 0 Multiply (4 + 5r) * (-5 + 2r) (4(-5 + 2r) + 5r * (-5 + 2r)) = 0 ((-5 * 4 + 2r * 4) + 5r * (-5 + 2r)) = 0 ((-20 + 8r) + 5r * (-5 + 2r)) = 0 (-20 + 8r + (-5 * 5r + 2r * 5r)) = 0 (-20 + 8r + (-25r + 10r2)) = 0 Combine like terms: 8r + -25r = -17r (-20 + -17r + 10r2) = 0 Solving -20 + -17r + 10r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -5r)(5 + -2r) = 0Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve: Simplifying -4 + -5r = 0 Solving -4 + -5r = 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 + -5r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5r = 0 + 4 -5r = 0 + 4 Combine like terms: 0 + 4 = 4 -5r = 4 Divide each side by '-5'. r = -0.8 Simplifying r = -0.8Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Solution
r = {-0.8, 2.5}
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