(5a-3b)(5a+9b)=

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Solution for (5a-3b)(5a+9b)= equation: 


Simplifying
(5a + -3b)(5a + 9b) = 0

Multiply (5a + -3b) * (5a + 9b)
(5a * (5a + 9b) + -3b * (5a + 9b)) = 0
((5a * 5a + 9b * 5a) + -3b * (5a + 9b)) = 0

Reorder the terms:
((45ab + 25a2) + -3b * (5a + 9b)) = 0
((45ab + 25a2) + -3b * (5a + 9b)) = 0
(45ab + 25a2 + (5a * -3b + 9b * -3b)) = 0
(45ab + 25a2 + (-15ab + -27b2)) = 0

Reorder the terms:
(45ab + -15ab + 25a2 + -27b2) = 0

Combine like terms: 45ab + -15ab = 30ab
(30ab + 25a2 + -27b2) = 0

Solving
30ab + 25a2 + -27b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -3b)(5a + 9b) = 0


Subproblem 1
Set the factor '(5a + -3b)' equal to zero and attempt to solve:

Simplifying
5a + -3b = 0

Solving
5a + -3b = 0

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

Add '3b' to each side of the equation.
5a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
5a + 0 = 0 + 3b
5a = 0 + 3b
Remove the zero:
5a = 3b

Divide each side by '5'.
a = 0.6b

Simplifying
a = 0.6b

Subproblem 2
Set the factor '(5a + 9b)' equal to zero and attempt to solve:

Simplifying
5a + 9b = 0

Solving
5a + 9b = 0

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

Add '-9b' to each side of the equation.
5a + 9b + -9b = 0 + -9b

Combine like terms: 9b + -9b = 0
5a + 0 = 0 + -9b
5a = 0 + -9b
Remove the zero:
5a = -9b

Divide each side by '5'.
a = -1.8b

Simplifying
a = -1.8b
Solution
a = {0.6b, -1.8b}

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