2r(r-7)+8r=56

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Solution for 2r(r-7)+8r=56 equation:


Simplifying
2r(r + -7) + 8r = 56

Reorder the terms:
2r(-7 + r) + 8r = 56
(-7 * 2r + r * 2r) + 8r = 56
(-14r + 2r2) + 8r = 56

Reorder the terms:
-14r + 8r + 2r2 = 56

Combine like terms: -14r + 8r = -6r
-6r + 2r2 = 56

Solving
-6r + 2r2 = 56

Solving for variable 'r'.

Reorder the terms:
-56 + -6r + 2r2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -6r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + -3r + r2) = 0

Factor a trinomial.
2((-4 + -1r)(7 + -1r)) = 0

Ignore the factor 2.

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 '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7

Solution

r = {-4, 7}

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