(5a+5b)(3a+4b)=

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Solution for (5a+5b)(3a+4b)= equation: 


Simplifying
(5a + 5b)(3a + 4b) = 0

Multiply (5a + 5b) * (3a + 4b)
(5a * (3a + 4b) + 5b * (3a + 4b)) = 0
((3a * 5a + 4b * 5a) + 5b * (3a + 4b)) = 0

Reorder the terms:
((20ab + 15a2) + 5b * (3a + 4b)) = 0
((20ab + 15a2) + 5b * (3a + 4b)) = 0
(20ab + 15a2 + (3a * 5b + 4b * 5b)) = 0
(20ab + 15a2 + (15ab + 20b2)) = 0

Reorder the terms:
(20ab + 15ab + 15a2 + 20b2) = 0

Combine like terms: 20ab + 15ab = 35ab
(35ab + 15a2 + 20b2) = 0

Solving
35ab + 15a2 + 20b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7ab + 3a2 + 4b2) = 0

Factor a trinomial.
5((a + b)(3a + 4b)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(3a + 4b)' equal to zero and attempt to solve:

Simplifying
3a + 4b = 0

Solving
3a + 4b = 0

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

Add '-4b' to each side of the equation.
3a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
3a + 0 = 0 + -4b
3a = 0 + -4b
Remove the zero:
3a = -4b

Divide each side by '3'.
a = -1.333333333b

Simplifying
a = -1.333333333b
Solution
a = {-1b, -1.333333333b}

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