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Simplifying (2r + -7)(2r + 3) = 0 Reorder the terms: (-7 + 2r)(2r + 3) = 0 Reorder the terms: (-7 + 2r)(3 + 2r) = 0 Multiply (-7 + 2r) * (3 + 2r) (-7(3 + 2r) + 2r * (3 + 2r)) = 0 ((3 * -7 + 2r * -7) + 2r * (3 + 2r)) = 0 ((-21 + -14r) + 2r * (3 + 2r)) = 0 (-21 + -14r + (3 * 2r + 2r * 2r)) = 0 (-21 + -14r + (6r + 4r2)) = 0 Combine like terms: -14r + 6r = -8r (-21 + -8r + 4r2) = 0 Solving -21 + -8r + 4r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -2r)(7 + -2r) = 0Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve: Simplifying -3 + -2r = 0 Solving -3 + -2r = 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 + -2r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2r = 0 + 3 -2r = 0 + 3 Combine like terms: 0 + 3 = 3 -2r = 3 Divide each side by '-2'. r = -1.5 Simplifying r = -1.5Subproblem 2
Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 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 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5Solution
r = {-1.5, 3.5}
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