(3r+2)(r-1)=-(7r-7)

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Solution for (3r+2)(r-1)=-(7r-7) equation: 


Simplifying
(3r + 2)(r + -1) = -1(7r + -7)

Reorder the terms:
(2 + 3r)(r + -1) = -1(7r + -7)

Reorder the terms:
(2 + 3r)(-1 + r) = -1(7r + -7)

Multiply (2 + 3r) * (-1 + r)
(2(-1 + r) + 3r * (-1 + r)) = -1(7r + -7)
((-1 * 2 + r * 2) + 3r * (-1 + r)) = -1(7r + -7)
((-2 + 2r) + 3r * (-1 + r)) = -1(7r + -7)
(-2 + 2r + (-1 * 3r + r * 3r)) = -1(7r + -7)
(-2 + 2r + (-3r + 3r2)) = -1(7r + -7)

Combine like terms: 2r + -3r = -1r
(-2 + -1r + 3r2) = -1(7r + -7)

Reorder the terms:
-2 + -1r + 3r2 = -1(-7 + 7r)
-2 + -1r + 3r2 = (-7 * -1 + 7r * -1)
-2 + -1r + 3r2 = (7 + -7r)

Solving
-2 + -1r + 3r2 = 7 + -7r

Solving for variable 'r'.

Reorder the terms:
-2 + -7 + -1r + 7r + 3r2 = 7 + -7r + -7 + 7r

Combine like terms: -2 + -7 = -9
-9 + -1r + 7r + 3r2 = 7 + -7r + -7 + 7r

Combine like terms: -1r + 7r = 6r
-9 + 6r + 3r2 = 7 + -7r + -7 + 7r

Reorder the terms:
-9 + 6r + 3r2 = 7 + -7 + -7r + 7r

Combine like terms: 7 + -7 = 0
-9 + 6r + 3r2 = 0 + -7r + 7r
-9 + 6r + 3r2 = -7r + 7r

Combine like terms: -7r + 7r = 0
-9 + 6r + 3r2 = 0

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

Factor a trinomial.
3((-3 + -1r)(1 + -1r)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3

Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-3, 1}

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