(8r-7)(r+7)-(3r-1)(r+7)=

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Solution for (8r-7)(r+7)-(3r-1)(r+7)= equation:


Simplifying
(8r + -7)(r + 7) + -1(3r + -1)(r + 7) = 0

Reorder the terms:
(-7 + 8r)(r + 7) + -1(3r + -1)(r + 7) = 0

Reorder the terms:
(-7 + 8r)(7 + r) + -1(3r + -1)(r + 7) = 0

Multiply (-7 + 8r) * (7 + r)
(-7(7 + r) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0
((7 * -7 + r * -7) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0
((-49 + -7r) + 8r * (7 + r)) + -1(3r + -1)(r + 7) = 0
(-49 + -7r + (7 * 8r + r * 8r)) + -1(3r + -1)(r + 7) = 0
(-49 + -7r + (56r + 8r2)) + -1(3r + -1)(r + 7) = 0

Combine like terms: -7r + 56r = 49r
(-49 + 49r + 8r2) + -1(3r + -1)(r + 7) = 0

Reorder the terms:
-49 + 49r + 8r2 + -1(-1 + 3r)(r + 7) = 0

Reorder the terms:
-49 + 49r + 8r2 + -1(-1 + 3r)(7 + r) = 0

Multiply (-1 + 3r) * (7 + r)
-49 + 49r + 8r2 + -1(-1(7 + r) + 3r * (7 + r)) = 0
-49 + 49r + 8r2 + -1((7 * -1 + r * -1) + 3r * (7 + r)) = 0
-49 + 49r + 8r2 + -1((-7 + -1r) + 3r * (7 + r)) = 0
-49 + 49r + 8r2 + -1(-7 + -1r + (7 * 3r + r * 3r)) = 0
-49 + 49r + 8r2 + -1(-7 + -1r + (21r + 3r2)) = 0

Combine like terms: -1r + 21r = 20r
-49 + 49r + 8r2 + -1(-7 + 20r + 3r2) = 0
-49 + 49r + 8r2 + (-7 * -1 + 20r * -1 + 3r2 * -1) = 0
-49 + 49r + 8r2 + (7 + -20r + -3r2) = 0

Reorder the terms:
-49 + 7 + 49r + -20r + 8r2 + -3r2 = 0

Combine like terms: -49 + 7 = -42
-42 + 49r + -20r + 8r2 + -3r2 = 0

Combine like terms: 49r + -20r = 29r
-42 + 29r + 8r2 + -3r2 = 0

Combine like terms: 8r2 + -3r2 = 5r2
-42 + 29r + 5r2 = 0

Solving
-42 + 29r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -1r)(6 + -5r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -5r)' equal to zero and attempt to solve: Simplifying 6 + -5r = 0 Solving 6 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5r = 0 + -6 -5r = 0 + -6 Combine like terms: 0 + -6 = -6 -5r = -6 Divide each side by '-5'. r = 1.2 Simplifying r = 1.2

Solution

r = {-7, 1.2}

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