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Simplifying -21 + -1r = -6r + -4r2 Solving -21 + -1r = -6r + -4r2 Solving for variable 'r'. Combine like terms: -1r + 6r = 5r -21 + 5r + 4r2 = -6r + -4r2 + 6r + 4r2 Reorder the terms: -21 + 5r + 4r2 = -6r + 6r + -4r2 + 4r2 Combine like terms: -6r + 6r = 0 -21 + 5r + 4r2 = 0 + -4r2 + 4r2 -21 + 5r + 4r2 = -4r2 + 4r2 Combine like terms: -4r2 + 4r2 = 0 -21 + 5r + 4r2 = 0 Factor a trinomial. (-3 + -1r)(7 + -4r) = 0Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 2
Set the factor '(7 + -4r)' equal to zero and attempt to solve: Simplifying 7 + -4r = 0 Solving 7 + -4r = 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 + -4r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4r = 0 + -7 -4r = 0 + -7 Combine like terms: 0 + -7 = -7 -4r = -7 Divide each side by '-4'. r = 1.75 Simplifying r = 1.75Solution
r = {-3, 1.75}
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