(3a+5b)(5b-3a)=

Solution for (3a+5b)(5b-3a)= equation:

Simplifying
(3a + 5b)(5b + -3a) = 0

Reorder the terms:
(3a + 5b)(-3a + 5b) = 0

Multiply (3a + 5b) * (-3a + 5b)
(3a * (-3a + 5b) + 5b * (-3a + 5b)) = 0
((-3a * 3a + 5b * 3a) + 5b * (-3a + 5b)) = 0

Reorder the terms:
((15ab + -9a2) + 5b * (-3a + 5b)) = 0
((15ab + -9a2) + 5b * (-3a + 5b)) = 0
(15ab + -9a2 + (-3a * 5b + 5b * 5b)) = 0
(15ab + -9a2 + (-15ab + 25b2)) = 0

Reorder the terms:
(15ab + -15ab + -9a2 + 25b2) = 0

Combine like terms: 15ab + -15ab = 0
(0 + -9a2 + 25b2) = 0
(-9a2 + 25b2) = 0

Solving
-9a2 + 25b2 = 0

Solving for variable 'a'.

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

Add '-25b2' to each side of the equation.
-9a2 + 25b2 + -25b2 = 0 + -25b2

Combine like terms: 25b2 + -25b2 = 0
-9a2 + 0 = 0 + -25b2
-9a2 = 0 + -25b2
Remove the zero:
-9a2 = -25b2

Divide each side by '-9'.
a2 = 2.777777778b2

Simplifying
a2 = 2.777777778b2

Take the square root of each side:
a = {-1.666666667b, 1.666666667b}