12r-5r^2=7

Solution for 12r-5r^2=7 equation:

Simplifying
12r + -5r2 = 7

Solving
12r + -5r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + 12r + -5r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 12r + -5r2 = 0

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

Subproblem 1
Set the factor '(-7 + 5r)' equal to zero and attempt to solve:

Simplifying
-7 + 5r = 0

Solving
-7 + 5r = 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 + 5r = 0 + 7

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

Combine like terms: 0 + 7 = 7
5r = 7

Divide each side by '5'.
r = 1.4

Simplifying
r = 1.4
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 = {1.4, 1}