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

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


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

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

Reorder the terms:
((10ab + 8a2) + -3b * (4a + 5b)) = 0
((10ab + 8a2) + -3b * (4a + 5b)) = 0
(10ab + 8a2 + (4a * -3b + 5b * -3b)) = 0
(10ab + 8a2 + (-12ab + -15b2)) = 0

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

Combine like terms: 10ab + -12ab = -2ab
(-2ab + 8a2 + -15b2) = 0

Solving
-2ab + 8a2 + -15b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(4a + 5b) = 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 '(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
Solution
a = {1.5b, -1.25b}

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