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Simplifying (5r + 4)(r + -7) = 0 Reorder the terms: (4 + 5r)(r + -7) = 0 Reorder the terms: (4 + 5r)(-7 + r) = 0 Multiply (4 + 5r) * (-7 + r) (4(-7 + r) + 5r * (-7 + r)) = 0 ((-7 * 4 + r * 4) + 5r * (-7 + r)) = 0 ((-28 + 4r) + 5r * (-7 + r)) = 0 (-28 + 4r + (-7 * 5r + r * 5r)) = 0 (-28 + 4r + (-35r + 5r2)) = 0 Combine like terms: 4r + -35r = -31r (-28 + -31r + 5r2) = 0 Solving -28 + -31r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -5r)(7 + -1r) = 0Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve: Simplifying -4 + -5r = 0 Solving -4 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5r = 0 + 4 -5r = 0 + 4 Combine like terms: 0 + 4 = 4 -5r = 4 Divide each side by '-5'. r = -0.8 Simplifying r = -0.8Subproblem 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 = {-0.8, 7}
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