(3a+2b)(4a-5b)=0

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Solution for (3a+2b)(4a-5b)=0 equation: 


Simplifying
(3a + 2b)(4a + -5b) = 0

Multiply (3a + 2b) * (4a + -5b)
(3a * (4a + -5b) + 2b * (4a + -5b)) = 0
((4a * 3a + -5b * 3a) + 2b * (4a + -5b)) = 0

Reorder the terms:
((-15ab + 12a2) + 2b * (4a + -5b)) = 0
((-15ab + 12a2) + 2b * (4a + -5b)) = 0
(-15ab + 12a2 + (4a * 2b + -5b * 2b)) = 0
(-15ab + 12a2 + (8ab + -10b2)) = 0

Reorder the terms:
(-15ab + 8ab + 12a2 + -10b2) = 0

Combine like terms: -15ab + 8ab = -7ab
(-7ab + 12a2 + -10b2) = 0

Solving
-7ab + 12a2 + -10b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -5b)(3a + 2b) = 0


Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b

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

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

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

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

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {1.25b, -0.6666666667b}

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