(r-2)(r+3)=(r-2)(2r+5)

Solution for (r-2)(r+3)=(r-2)(2r+5) equation:

Simplifying
(r + -2)(r + 3) = (r + -2)(2r + 5)

Reorder the terms:
(-2 + r)(r + 3) = (r + -2)(2r + 5)

Reorder the terms:
(-2 + r)(3 + r) = (r + -2)(2r + 5)

Multiply (-2 + r) * (3 + r)
(-2(3 + r) + r(3 + r)) = (r + -2)(2r + 5)
((3 * -2 + r * -2) + r(3 + r)) = (r + -2)(2r + 5)
((-6 + -2r) + r(3 + r)) = (r + -2)(2r + 5)
(-6 + -2r + (3 * r + r * r)) = (r + -2)(2r + 5)
(-6 + -2r + (3r + r2)) = (r + -2)(2r + 5)

Combine like terms: -2r + 3r = 1r
(-6 + 1r + r2) = (r + -2)(2r + 5)

Reorder the terms:
-6 + 1r + r2 = (-2 + r)(2r + 5)

Reorder the terms:
-6 + 1r + r2 = (-2 + r)(5 + 2r)

Multiply (-2 + r) * (5 + 2r)
-6 + 1r + r2 = (-2(5 + 2r) + r(5 + 2r))
-6 + 1r + r2 = ((5 * -2 + 2r * -2) + r(5 + 2r))
-6 + 1r + r2 = ((-10 + -4r) + r(5 + 2r))
-6 + 1r + r2 = (-10 + -4r + (5 * r + 2r * r))
-6 + 1r + r2 = (-10 + -4r + (5r + 2r2))

Combine like terms: -4r + 5r = 1r
-6 + 1r + r2 = (-10 + 1r + 2r2)

Add '-1r' to each side of the equation.
-6 + 1r + -1r + r2 = -10 + 1r + -1r + 2r2

Combine like terms: 1r + -1r = 0
-6 + 0 + r2 = -10 + 1r + -1r + 2r2
-6 + r2 = -10 + 1r + -1r + 2r2

Combine like terms: 1r + -1r = 0
-6 + r2 = -10 + 0 + 2r2
-6 + r2 = -10 + 2r2

Solving
-6 + r2 = -10 + 2r2

Solving for variable 'r'.

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

Add '-2r2' to each side of the equation.
-6 + r2 + -2r2 = -10 + 2r2 + -2r2

Combine like terms: r2 + -2r2 = -1r2
-6 + -1r2 = -10 + 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-6 + -1r2 = -10 + 0
-6 + -1r2 = -10

Add '6' to each side of the equation.
-6 + 6 + -1r2 = -10 + 6

Combine like terms: -6 + 6 = 0
0 + -1r2 = -10 + 6
-1r2 = -10 + 6

Combine like terms: -10 + 6 = -4
-1r2 = -4

Divide each side by '-1'.
r2 = 4

Simplifying
r2 = 4

Take the square root of each side:
r = {-2, 2}