24r^2+219r+263=-5r+7

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Solution for 24r^2+219r+263=-5r+7 equation: 


Simplifying
24r2 + 219r + 263 = -5r + 7

Reorder the terms:
263 + 219r + 24r2 = -5r + 7

Reorder the terms:
263 + 219r + 24r2 = 7 + -5r

Solving
263 + 219r + 24r2 = 7 + -5r

Solving for variable 'r'.

Reorder the terms:
263 + -7 + 219r + 5r + 24r2 = 7 + -5r + -7 + 5r

Combine like terms: 263 + -7 = 256
256 + 219r + 5r + 24r2 = 7 + -5r + -7 + 5r

Combine like terms: 219r + 5r = 224r
256 + 224r + 24r2 = 7 + -5r + -7 + 5r

Reorder the terms:
256 + 224r + 24r2 = 7 + -7 + -5r + 5r

Combine like terms: 7 + -7 = 0
256 + 224r + 24r2 = 0 + -5r + 5r
256 + 224r + 24r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
256 + 224r + 24r2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(32 + 28r + 3r2) = 0

Factor a trinomial.
8((8 + r)(4 + 3r)) = 0

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + 3r)' equal to zero and attempt to solve:

Simplifying
4 + 3r = 0

Solving
4 + 3r = 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 + 3r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3r = 0 + -4
3r = 0 + -4

Combine like terms: 0 + -4 = -4
3r = -4

Divide each side by '3'.
r = -1.333333333

Simplifying
r = -1.333333333
Solution
r = {-8, -1.333333333}

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