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

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

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

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

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

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

Combine like terms: 3r + -8r = -5r
0 = (-3 + -5r + 8r2)

Solving
0 = -3 + -5r + 8r2

Solving for variable 'r'.

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

Reorder the terms:
3 + 5r + -8r2 = -3 + 3 + -5r + 5r + 8r2 + -8r2

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

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

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

Factor a trinomial.
(1 + -1r)(3 + 8r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 8r)' equal to zero and attempt to solve:

Simplifying
3 + 8r = 0

Solving
3 + 8r = 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 + 8r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8r = 0 + -3
8r = 0 + -3

Combine like terms: 0 + -3 = -3
8r = -3

Divide each side by '8'.
r = -0.375

Simplifying
r = -0.375
Solution
r = {1, -0.375}