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Simplifying r(r + 5) + -84 = 0 Reorder the terms: r(5 + r) + -84 = 0 (5 * r + r * r) + -84 = 0 (5r + r2) + -84 = 0 Reorder the terms: -84 + 5r + r2 = 0 Solving -84 + 5r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-12 + -1r)(7 + -1r) = 0Subproblem 1
Set the factor '(-12 + -1r)' equal to zero and attempt to solve: Simplifying -12 + -1r = 0 Solving -12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1r = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1r = 0 + 12 -1r = 0 + 12 Combine like terms: 0 + 12 = 12 -1r = 12 Divide each side by '-1'. r = -12 Simplifying r = -12Subproblem 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 = {-12, 7}
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