7r=3-6r^2

Solution for 7r=3-6r^2 equation:

Simplifying
7r = 3 + -6r2

Solving
7r = 3 + -6r2

Solving for variable 'r'.

Reorder the terms:
-3 + 7r + 6r2 = 3 + -6r2 + -3 + 6r2

Reorder the terms:
-3 + 7r + 6r2 = 3 + -3 + -6r2 + 6r2

Combine like terms: 3 + -3 = 0
-3 + 7r + 6r2 = 0 + -6r2 + 6r2
-3 + 7r + 6r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
-3 + 7r + 6r2 = 0

Factor a trinomial.
(-3 + -2r)(1 + -3r) = 0

Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve:

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {-1.5, 0.3333333333}