2(r+2)(r+2)=72

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Solution for 2(r+2)(r+2)=72 equation:


Simplifying
2(r + 2)(r + 2) = 72

Reorder the terms:
2(2 + r)(r + 2) = 72

Reorder the terms:
2(2 + r)(2 + r) = 72

Multiply (2 + r) * (2 + r)
2(2(2 + r) + r(2 + r)) = 72
2((2 * 2 + r * 2) + r(2 + r)) = 72
2((4 + 2r) + r(2 + r)) = 72
2(4 + 2r + (2 * r + r * r)) = 72
2(4 + 2r + (2r + r2)) = 72

Combine like terms: 2r + 2r = 4r
2(4 + 4r + r2) = 72
(4 * 2 + 4r * 2 + r2 * 2) = 72
(8 + 8r + 2r2) = 72

Solving
8 + 8r + 2r2 = 72

Solving for variable 'r'.

Reorder the terms:
8 + -72 + 8r + 2r2 = 72 + -72

Combine like terms: 8 + -72 = -64
-64 + 8r + 2r2 = 72 + -72

Combine like terms: 72 + -72 = 0
-64 + 8r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4r + r2) = 0

Factor a trinomial.
2((-8 + -1r)(4 + -1r)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-8 + -1r)' equal to zero and attempt to solve: Simplifying -8 + -1r = 0 Solving -8 + -1r = 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 + -1r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1r = 0 + 8 -1r = 0 + 8 Combine like terms: 0 + 8 = 8 -1r = 8 Divide each side by '-1'. r = -8 Simplifying r = -8

Subproblem 2

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

Solution

r = {-8, 4}

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