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Simplifying (7r + -2)(5r + 2) = 0 Reorder the terms: (-2 + 7r)(5r + 2) = 0 Reorder the terms: (-2 + 7r)(2 + 5r) = 0 Multiply (-2 + 7r) * (2 + 5r) (-2(2 + 5r) + 7r * (2 + 5r)) = 0 ((2 * -2 + 5r * -2) + 7r * (2 + 5r)) = 0 ((-4 + -10r) + 7r * (2 + 5r)) = 0 (-4 + -10r + (2 * 7r + 5r * 7r)) = 0 (-4 + -10r + (14r + 35r2)) = 0 Combine like terms: -10r + 14r = 4r (-4 + 4r + 35r2) = 0 Solving -4 + 4r + 35r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -5r)(2 + -7r) = 0Subproblem 1
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 = -0.4Subproblem 2
Set the factor '(2 + -7r)' equal to zero and attempt to solve: Simplifying 2 + -7r = 0 Solving 2 + -7r = 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 + -7r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7r = 0 + -2 -7r = 0 + -2 Combine like terms: 0 + -2 = -2 -7r = -2 Divide each side by '-7'. r = 0.2857142857 Simplifying r = 0.2857142857Solution
r = {-0.4, 0.2857142857}
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