2(2r-3)(2r+3)=0

Solution for 2(2r-3)(2r+3)=0 equation:

Simplifying
2(2r + -3)(2r + 3) = 0

Reorder the terms:
2(-3 + 2r)(2r + 3) = 0

Reorder the terms:
2(-3 + 2r)(3 + 2r) = 0

Multiply (-3 + 2r) * (3 + 2r)
2(-3(3 + 2r) + 2r * (3 + 2r)) = 0
2((3 * -3 + 2r * -3) + 2r * (3 + 2r)) = 0
2((-9 + -6r) + 2r * (3 + 2r)) = 0
2(-9 + -6r + (3 * 2r + 2r * 2r)) = 0
2(-9 + -6r + (6r + 4r2)) = 0

Combine like terms: -6r + 6r = 0
2(-9 + 0 + 4r2) = 0
2(-9 + 4r2) = 0
(-9 * 2 + 4r2 * 2) = 0
(-18 + 8r2) = 0

Solving
-18 + 8r2 = 0

Solving for variable 'r'.

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

Add '18' to each side of the equation.
-18 + 18 + 8r2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 8r2 = 0 + 18
8r2 = 0 + 18

Combine like terms: 0 + 18 = 18
8r2 = 18

Divide each side by '8'.
r2 = 2.25

Simplifying
r2 = 2.25

Take the square root of each side:
r = {-1.5, 1.5}