8r^2+3r+2=7

Solution for 8r^2+3r+2=7 equation:

Simplifying
8r2 + 3r + 2 = 7

Reorder the terms:
2 + 3r + 8r2 = 7

Solving
2 + 3r + 8r2 = 7

Solving for variable 'r'.

Reorder the terms:
2 + -7 + 3r + 8r2 = 7 + -7

Combine like terms: 2 + -7 = -5
-5 + 3r + 8r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-5 + 3r + 8r2 = 0

Factor a trinomial.
(-1 + -1r)(5 + -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 '(5 + -8r)' equal to zero and attempt to solve:

Simplifying
5 + -8r = 0

Solving
5 + -8r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8r = 0 + -5

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

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

Divide each side by '-8'.
r = 0.625

Simplifying
r = 0.625
Solution
r = {-1, 0.625}