(5r+7)(r-3)=-(23r-69)

Solution for (5r+7)(r-3)=-(23r-69) equation:

Simplifying
(5r + 7)(r + -3) = -1(23r + -69)

Reorder the terms:
(7 + 5r)(r + -3) = -1(23r + -69)

Reorder the terms:
(7 + 5r)(-3 + r) = -1(23r + -69)

Multiply (7 + 5r) * (-3 + r)
(7(-3 + r) + 5r * (-3 + r)) = -1(23r + -69)
((-3 * 7 + r * 7) + 5r * (-3 + r)) = -1(23r + -69)
((-21 + 7r) + 5r * (-3 + r)) = -1(23r + -69)
(-21 + 7r + (-3 * 5r + r * 5r)) = -1(23r + -69)
(-21 + 7r + (-15r + 5r2)) = -1(23r + -69)

Combine like terms: 7r + -15r = -8r
(-21 + -8r + 5r2) = -1(23r + -69)

Reorder the terms:
-21 + -8r + 5r2 = -1(-69 + 23r)
-21 + -8r + 5r2 = (-69 * -1 + 23r * -1)
-21 + -8r + 5r2 = (69 + -23r)

Solving
-21 + -8r + 5r2 = 69 + -23r

Solving for variable 'r'.

Reorder the terms:
-21 + -69 + -8r + 23r + 5r2 = 69 + -23r + -69 + 23r

Combine like terms: -21 + -69 = -90
-90 + -8r + 23r + 5r2 = 69 + -23r + -69 + 23r

Combine like terms: -8r + 23r = 15r
-90 + 15r + 5r2 = 69 + -23r + -69 + 23r

Reorder the terms:
-90 + 15r + 5r2 = 69 + -69 + -23r + 23r

Combine like terms: 69 + -69 = 0
-90 + 15r + 5r2 = 0 + -23r + 23r
-90 + 15r + 5r2 = -23r + 23r

Combine like terms: -23r + 23r = 0
-90 + 15r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + 3r + r2) = 0

Factor a trinomial.
5((-6 + -1r)(3 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 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 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
Subproblem 2
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
Solution
r = {-6, 3}