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Simplifying (4r + 1)(5r + -7) = 0 Reorder the terms: (1 + 4r)(5r + -7) = 0 Reorder the terms: (1 + 4r)(-7 + 5r) = 0 Multiply (1 + 4r) * (-7 + 5r) (1(-7 + 5r) + 4r * (-7 + 5r)) = 0 ((-7 * 1 + 5r * 1) + 4r * (-7 + 5r)) = 0 ((-7 + 5r) + 4r * (-7 + 5r)) = 0 (-7 + 5r + (-7 * 4r + 5r * 4r)) = 0 (-7 + 5r + (-28r + 20r2)) = 0 Combine like terms: 5r + -28r = -23r (-7 + -23r + 20r2) = 0 Solving -7 + -23r + 20r2 = 0 Solving for variable 'r'. Factor a trinomial. (-1 + -4r)(7 + -5r) = 0Subproblem 1
Set the factor '(-1 + -4r)' equal to zero and attempt to solve: Simplifying -1 + -4r = 0 Solving -1 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4r = 0 + 1 -4r = 0 + 1 Combine like terms: 0 + 1 = 1 -4r = 1 Divide each side by '-4'. r = -0.25 Simplifying r = -0.25Subproblem 2
Set the factor '(7 + -5r)' equal to zero and attempt to solve: Simplifying 7 + -5r = 0 Solving 7 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5r = 0 + -7 -5r = 0 + -7 Combine like terms: 0 + -7 = -7 -5r = -7 Divide each side by '-5'. r = 1.4 Simplifying r = 1.4Solution
r = {-0.25, 1.4}
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