7r(6r-5)=7

Solution for 7r(6r-5)=7 equation:

Simplifying
7r(6r + -5) = 7

Reorder the terms:
7r(-5 + 6r) = 7
(-5 * 7r + 6r * 7r) = 7
(-35r + 42r2) = 7

Solving
-35r + 42r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + -35r + 42r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -35r + 42r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + -5r + 6r2) = 0

Factor a trinomial.
7((-1 + -6r)(1 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-1 + -6r)' equal to zero and attempt to solve:

Simplifying
-1 + -6r = 0

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

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

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

Divide each side by '-6'.
r = -0.1666666667

Simplifying
r = -0.1666666667
Subproblem 2
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
Solution
r = {-0.1666666667, 1}