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

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

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

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

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

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

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

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

Solving
-4a2 + 9b2 = 0

Solving for variable 'a'.

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

Add '-9b2' to each side of the equation.
-4a2 + 9b2 + -9b2 = 0 + -9b2

Combine like terms: 9b2 + -9b2 = 0
-4a2 + 0 = 0 + -9b2
-4a2 = 0 + -9b2
Remove the zero:
-4a2 = -9b2

Divide each side by '-4'.
a2 = 2.25b2

Simplifying
a2 = 2.25b2

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