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Simplifying (r + 7)(r + -12) = 0 Reorder the terms: (7 + r)(r + -12) = 0 Reorder the terms: (7 + r)(-12 + r) = 0 Multiply (7 + r) * (-12 + r) (7(-12 + r) + r(-12 + r)) = 0 ((-12 * 7 + r * 7) + r(-12 + r)) = 0 ((-84 + 7r) + r(-12 + r)) = 0 (-84 + 7r + (-12 * r + r * r)) = 0 (-84 + 7r + (-12r + r2)) = 0 Combine like terms: 7r + -12r = -5r (-84 + -5r + r2) = 0 Solving -84 + -5r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -1r)(12 + -1r) = 0Subproblem 1
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 = -7Subproblem 2
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 = 12Solution
r = {-7, 12}
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