(3a+3b)(7a-5b)=

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Solution for (3a+3b)(7a-5b)= equation: 


Simplifying
(3a + 3b)(7a + -5b) = 0

Multiply (3a + 3b) * (7a + -5b)
(3a * (7a + -5b) + 3b * (7a + -5b)) = 0
((7a * 3a + -5b * 3a) + 3b * (7a + -5b)) = 0

Reorder the terms:
((-15ab + 21a2) + 3b * (7a + -5b)) = 0
((-15ab + 21a2) + 3b * (7a + -5b)) = 0
(-15ab + 21a2 + (7a * 3b + -5b * 3b)) = 0
(-15ab + 21a2 + (21ab + -15b2)) = 0

Reorder the terms:
(-15ab + 21ab + 21a2 + -15b2) = 0

Combine like terms: -15ab + 21ab = 6ab
(6ab + 21a2 + -15b2) = 0

Solving
6ab + 21a2 + -15b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2ab + 7a2 + -5b2) = 0

Factor a trinomial.
3((7a + -5b)(a + b)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7a + -5b)' equal to zero and attempt to solve:

Simplifying
7a + -5b = 0

Solving
7a + -5b = 0

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

Add '5b' to each side of the equation.
7a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
7a + 0 = 0 + 5b
7a = 0 + 5b
Remove the zero:
7a = 5b

Divide each side by '7'.
a = 0.7142857143b

Simplifying
a = 0.7142857143b

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

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {0.7142857143b, -1b}

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