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Simplifying 2r2 + -4r + -12 = r2 Reorder the terms: -12 + -4r + 2r2 = r2 Solving -12 + -4r + 2r2 = r2 Solving for variable 'r'. Combine like terms: 2r2 + -1r2 = 1r2 -12 + -4r + 1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -12 + -4r + 1r2 = 0 Factor a trinomial. (-2 + -1r)(6 + -1r) = 0Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 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 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve: Simplifying 6 + -1r = 0 Solving 6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1r = 0 + -6 -1r = 0 + -6 Combine like terms: 0 + -6 = -6 -1r = -6 Divide each side by '-1'. r = 6 Simplifying r = 6Solution
r = {-2, 6}
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