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Simplifying (r + 7)(5r + -2) = 0 Reorder the terms: (7 + r)(5r + -2) = 0 Reorder the terms: (7 + r)(-2 + 5r) = 0 Multiply (7 + r) * (-2 + 5r) (7(-2 + 5r) + r(-2 + 5r)) = 0 ((-2 * 7 + 5r * 7) + r(-2 + 5r)) = 0 ((-14 + 35r) + r(-2 + 5r)) = 0 (-14 + 35r + (-2 * r + 5r * r)) = 0 (-14 + 35r + (-2r + 5r2)) = 0 Combine like terms: 35r + -2r = 33r (-14 + 33r + 5r2) = 0 Solving -14 + 33r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -1r)(2 + -5r) = 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 '(2 + -5r)' equal to zero and attempt to solve: Simplifying 2 + -5r = 0 Solving 2 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5r = 0 + -2 -5r = 0 + -2 Combine like terms: 0 + -2 = -2 -5r = -2 Divide each side by '-5'. r = 0.4 Simplifying r = 0.4Solution
r = {-7, 0.4}
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