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

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


Simplifying
(2a + 5b)(a + -1b) = 0

Multiply (2a + 5b) * (a + -1b)
(2a * (a + -1b) + 5b * (a + -1b)) = 0
((a * 2a + -1b * 2a) + 5b * (a + -1b)) = 0

Reorder the terms:
((-2ab + 2a2) + 5b * (a + -1b)) = 0
((-2ab + 2a2) + 5b * (a + -1b)) = 0
(-2ab + 2a2 + (a * 5b + -1b * 5b)) = 0
(-2ab + 2a2 + (5ab + -5b2)) = 0

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

Combine like terms: -2ab + 5ab = 3ab
(3ab + 2a2 + -5b2) = 0

Solving
3ab + 2a2 + -5b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -1b)(2a + 5b) = 0


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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b

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 = {b, -2.5b}

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