r^2-[4-r(3-r)]=2(2r-3)

Solution for r^2-[4-r(3-r)]=2(2r-3) equation:

Simplifying
r2 + -1[4 + -1r(3 + -1r)] = 2(2r + -3)
r2 + -1[4 + (3 * -1r + -1r * -1r)] = 2(2r + -3)
r2 + -1[4 + (-3r + 1r2)] = 2(2r + -3)
r2 + [4 * -1 + -3r * -1 + 1r2 * -1] = 2(2r + -3)
r2 + [-4 + 3r + -1r2] = 2(2r + -3)

Reorder the terms:
-4 + 3r + r2 + -1r2 = 2(2r + -3)

Combine like terms: r2 + -1r2 = 0
-4 + 3r + 0 = 2(2r + -3)
-4 + 3r = 2(2r + -3)

Reorder the terms:
-4 + 3r = 2(-3 + 2r)
-4 + 3r = (-3 * 2 + 2r * 2)
-4 + 3r = (-6 + 4r)

Solving
-4 + 3r = -6 + 4r

Solving for variable 'r'.

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

Add '-4r' to each side of the equation.
-4 + 3r + -4r = -6 + 4r + -4r

Combine like terms: 3r + -4r = -1r
-4 + -1r = -6 + 4r + -4r

Combine like terms: 4r + -4r = 0
-4 + -1r = -6 + 0
-4 + -1r = -6

Add '4' to each side of the equation.
-4 + 4 + -1r = -6 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = -6 + 4
-1r = -6 + 4

Combine like terms: -6 + 4 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2