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Simplifying (2r + 5)(r + -7) = 0 Reorder the terms: (5 + 2r)(r + -7) = 0 Reorder the terms: (5 + 2r)(-7 + r) = 0 Multiply (5 + 2r) * (-7 + r) (5(-7 + r) + 2r * (-7 + r)) = 0 ((-7 * 5 + r * 5) + 2r * (-7 + r)) = 0 ((-35 + 5r) + 2r * (-7 + r)) = 0 (-35 + 5r + (-7 * 2r + r * 2r)) = 0 (-35 + 5r + (-14r + 2r2)) = 0 Combine like terms: 5r + -14r = -9r (-35 + -9r + 2r2) = 0 Solving -35 + -9r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -2r)(7 + -1r) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 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 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Solution
r = {-2.5, 7}
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