7r^2-4r=3r^2-1

Solution for 7r^2-4r=3r^2-1 equation:

Simplifying
7r2 + -4r = 3r2 + -1

Reorder the terms:
-4r + 7r2 = 3r2 + -1

Reorder the terms:
-4r + 7r2 = -1 + 3r2

Solving
-4r + 7r2 = -1 + 3r2

Solving for variable 'r'.

Reorder the terms:
1 + -4r + 7r2 + -3r2 = -1 + 3r2 + 1 + -3r2

Combine like terms: 7r2 + -3r2 = 4r2
1 + -4r + 4r2 = -1 + 3r2 + 1 + -3r2

Reorder the terms:
1 + -4r + 4r2 = -1 + 1 + 3r2 + -3r2

Combine like terms: -1 + 1 = 0
1 + -4r + 4r2 = 0 + 3r2 + -3r2
1 + -4r + 4r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
1 + -4r + 4r2 = 0

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

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {0.5, 0.5}