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

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


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

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

Reorder the terms:
((-5ab + 2a2) + 3b * (2a + -5b)) = 0
((-5ab + 2a2) + 3b * (2a + -5b)) = 0
(-5ab + 2a2 + (2a * 3b + -5b * 3b)) = 0
(-5ab + 2a2 + (6ab + -15b2)) = 0

Reorder the terms:
(-5ab + 6ab + 2a2 + -15b2) = 0

Combine like terms: -5ab + 6ab = 1ab
(1ab + 2a2 + -15b2) = 0

Solving
1ab + 2a2 + -15b2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

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

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {2.5b, -3b}

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