-r^2=6r-16

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Solution for -r^2=6r-16 equation:


Simplifying
-1r2 = 6r + -16

Reorder the terms:
-1r2 = -16 + 6r

Solving
-1r2 = -16 + 6r

Solving for variable 'r'.

Reorder the terms:
16 + -6r + -1r2 = -16 + 6r + 16 + -6r

Reorder the terms:
16 + -6r + -1r2 = -16 + 16 + 6r + -6r

Combine like terms: -16 + 16 = 0
16 + -6r + -1r2 = 0 + 6r + -6r
16 + -6r + -1r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
16 + -6r + -1r2 = 0

Factor a trinomial.
(2 + -1r)(8 + r) = 0

Subproblem 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 = 2

Subproblem 2

Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8

Solution

r = {2, -8}

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