(2a-3b)(3a+7b)=0

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Solution for (2a-3b)(3a+7b)=0 equation: 


Simplifying
(2a + -3b)(3a + 7b) = 0

Multiply (2a + -3b) * (3a + 7b)
(2a * (3a + 7b) + -3b * (3a + 7b)) = 0
((3a * 2a + 7b * 2a) + -3b * (3a + 7b)) = 0

Reorder the terms:
((14ab + 6a2) + -3b * (3a + 7b)) = 0
((14ab + 6a2) + -3b * (3a + 7b)) = 0
(14ab + 6a2 + (3a * -3b + 7b * -3b)) = 0
(14ab + 6a2 + (-9ab + -21b2)) = 0

Reorder the terms:
(14ab + -9ab + 6a2 + -21b2) = 0

Combine like terms: 14ab + -9ab = 5ab
(5ab + 6a2 + -21b2) = 0

Solving
5ab + 6a2 + -21b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(3a + 7b) = 0


Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b

Subproblem 2
Set the factor '(3a + 7b)' equal to zero and attempt to solve:

Simplifying
3a + 7b = 0

Solving
3a + 7b = 0

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

Add '-7b' to each side of the equation.
3a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
3a + 0 = 0 + -7b
3a = 0 + -7b
Remove the zero:
3a = -7b

Divide each side by '3'.
a = -2.333333333b

Simplifying
a = -2.333333333b
Solution
a = {1.5b, -2.333333333b}

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