r^2=8(r+6)

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Solution for r^2=8(r+6) equation:


Simplifying
r2 = 8(r + 6)

Reorder the terms:
r2 = 8(6 + r)
r2 = (6 * 8 + r * 8)
r2 = (48 + 8r)

Solving
r2 = 48 + 8r

Solving for variable 'r'.

Reorder the terms:
-48 + -8r + r2 = 48 + 8r + -48 + -8r

Reorder the terms:
-48 + -8r + r2 = 48 + -48 + 8r + -8r

Combine like terms: 48 + -48 = 0
-48 + -8r + r2 = 0 + 8r + -8r
-48 + -8r + r2 = 8r + -8r

Combine like terms: 8r + -8r = 0
-48 + -8r + r2 = 0

Factor a trinomial.
(-4 + -1r)(12 + -1r) = 0

Subproblem 1

Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 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 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4

Subproblem 2

Set the factor '(12 + -1r)' equal to zero and attempt to solve: Simplifying 12 + -1r = 0 Solving 12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1r = 0 + -12 -1r = 0 + -12 Combine like terms: 0 + -12 = -12 -1r = -12 Divide each side by '-1'. r = 12 Simplifying r = 12

Solution

r = {-4, 12}

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