(15a+13b)(5a-6b)=0

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Solution for (15a+13b)(5a-6b)=0 equation: 


Simplifying
(15a + 13b)(5a + -6b) = 0

Multiply (15a + 13b) * (5a + -6b)
(15a * (5a + -6b) + 13b * (5a + -6b)) = 0
((5a * 15a + -6b * 15a) + 13b * (5a + -6b)) = 0

Reorder the terms:
((-90ab + 75a2) + 13b * (5a + -6b)) = 0
((-90ab + 75a2) + 13b * (5a + -6b)) = 0
(-90ab + 75a2 + (5a * 13b + -6b * 13b)) = 0
(-90ab + 75a2 + (65ab + -78b2)) = 0

Reorder the terms:
(-90ab + 65ab + 75a2 + -78b2) = 0

Combine like terms: -90ab + 65ab = -25ab
(-25ab + 75a2 + -78b2) = 0

Solving
-25ab + 75a2 + -78b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -6b)(15a + 13b) = 0


Subproblem 1
Set the factor '(5a + -6b)' equal to zero and attempt to solve:

Simplifying
5a + -6b = 0

Solving
5a + -6b = 0

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

Add '6b' to each side of the equation.
5a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
5a + 0 = 0 + 6b
5a = 0 + 6b
Remove the zero:
5a = 6b

Divide each side by '5'.
a = 1.2b

Simplifying
a = 1.2b

Subproblem 2
Set the factor '(15a + 13b)' equal to zero and attempt to solve:

Simplifying
15a + 13b = 0

Solving
15a + 13b = 0

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

Add '-13b' to each side of the equation.
15a + 13b + -13b = 0 + -13b

Combine like terms: 13b + -13b = 0
15a + 0 = 0 + -13b
15a = 0 + -13b
Remove the zero:
15a = -13b

Divide each side by '15'.
a = -0.8666666667b

Simplifying
a = -0.8666666667b
Solution
a = {1.2b, -0.8666666667b}

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