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Simplifying (4r + -2)(5r + 4) = 0 Reorder the terms: (-2 + 4r)(5r + 4) = 0 Reorder the terms: (-2 + 4r)(4 + 5r) = 0 Multiply (-2 + 4r) * (4 + 5r) (-2(4 + 5r) + 4r * (4 + 5r)) = 0 ((4 * -2 + 5r * -2) + 4r * (4 + 5r)) = 0 ((-8 + -10r) + 4r * (4 + 5r)) = 0 (-8 + -10r + (4 * 4r + 5r * 4r)) = 0 (-8 + -10r + (16r + 20r2)) = 0 Combine like terms: -10r + 16r = 6r (-8 + 6r + 20r2) = 0 Solving -8 + 6r + 20r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3r + 10r2) = 0 Factor a trinomial. 2((-4 + -5r)(1 + -2r)) = 0 Ignore the factor 2.Subproblem 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 '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {-0.8, 0.5}
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