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

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


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

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

Reorder the terms:
((-8ab + 6a2) + 5b * (3a + -4b)) = 0
((-8ab + 6a2) + 5b * (3a + -4b)) = 0
(-8ab + 6a2 + (3a * 5b + -4b * 5b)) = 0
(-8ab + 6a2 + (15ab + -20b2)) = 0

Reorder the terms:
(-8ab + 15ab + 6a2 + -20b2) = 0

Combine like terms: -8ab + 15ab = 7ab
(7ab + 6a2 + -20b2) = 0

Solving
7ab + 6a2 + -20b2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(2a + 5b)' equal to zero and attempt to solve:

Simplifying
2a + 5b = 0

Solving
2a + 5b = 0

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

Add '-5b' to each side of the equation.
2a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
2a + 0 = 0 + -5b
2a = 0 + -5b
Remove the zero:
2a = -5b

Divide each side by '2'.
a = -2.5b

Simplifying
a = -2.5b
Solution
a = {1.333333333b, -2.5b}

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