r(10r+3)=7

Solution for r(10r+3)=7 equation:

Simplifying
r(10r + 3) = 7

Reorder the terms:
r(3 + 10r) = 7
(3 * r + 10r * r) = 7
(3r + 10r2) = 7

Solving
3r + 10r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + 3r + 10r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 3r + 10r2 = 0

Factor a trinomial.
(-1 + -1r)(7 + -10r) = 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 '(7 + -10r)' equal to zero and attempt to solve:

Simplifying
7 + -10r = 0

Solving
7 + -10r = 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 + -10r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10r = 0 + -7
-10r = 0 + -7

Combine like terms: 0 + -7 = -7
-10r = -7

Divide each side by '-10'.
r = 0.7

Simplifying
r = 0.7
Solution
r = {-1, 0.7}