7r^2-29r=5+5r

Solution for 7r^2-29r=5+5r equation:

Simplifying
7r2 + -29r = 5 + 5r

Reorder the terms:
-29r + 7r2 = 5 + 5r

Solving
-29r + 7r2 = 5 + 5r

Solving for variable 'r'.

Reorder the terms:
-5 + -29r + -5r + 7r2 = 5 + 5r + -5 + -5r

Combine like terms: -29r + -5r = -34r
-5 + -34r + 7r2 = 5 + 5r + -5 + -5r

Reorder the terms:
-5 + -34r + 7r2 = 5 + -5 + 5r + -5r

Combine like terms: 5 + -5 = 0
-5 + -34r + 7r2 = 0 + 5r + -5r
-5 + -34r + 7r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
-5 + -34r + 7r2 = 0

Factor a trinomial.
(-1 + -7r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-1 + -7r)' equal to zero and attempt to solve:

Simplifying
-1 + -7r = 0

Solving
-1 + -7r = 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 + -7r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7r = 0 + 1
-7r = 0 + 1

Combine like terms: 0 + 1 = 1
-7r = 1

Divide each side by '-7'.
r = -0.1428571429

Simplifying
r = -0.1428571429
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.1428571429, 5}