2(2a-3b)(2a+3b)=0

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

Simplifying
2(2a + -3b)(2a + 3b) = 0

Multiply (2a + -3b) * (2a + 3b)
2(2a * (2a + 3b) + -3b * (2a + 3b)) = 0
2((2a * 2a + 3b * 2a) + -3b * (2a + 3b)) = 0

Reorder the terms:
2((6ab + 4a2) + -3b * (2a + 3b)) = 0
2((6ab + 4a2) + -3b * (2a + 3b)) = 0
2(6ab + 4a2 + (2a * -3b + 3b * -3b)) = 0
2(6ab + 4a2 + (-6ab + -9b2)) = 0

Reorder the terms:
2(6ab + -6ab + 4a2 + -9b2) = 0

Combine like terms: 6ab + -6ab = 0
2(0 + 4a2 + -9b2) = 0
2(4a2 + -9b2) = 0
(4a2 * 2 + -9b2 * 2) = 0
(8a2 + -18b2) = 0

Solving
8a2 + -18b2 = 0

Solving for variable 'a'.

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

Add '18b2' to each side of the equation.
8a2 + -18b2 + 18b2 = 0 + 18b2

Combine like terms: -18b2 + 18b2 = 0
8a2 + 0 = 0 + 18b2
8a2 = 0 + 18b2
Remove the zero:
8a2 = 18b2

Divide each side by '8'.
a2 = 2.25b2

Simplifying
a2 = 2.25b2

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