(a+2b)(2a-b)=0

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


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

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

Reorder the terms:
((-1ab + 2a2) + 2b * (2a + -1b)) = 0
((-1ab + 2a2) + 2b * (2a + -1b)) = 0
(-1ab + 2a2 + (2a * 2b + -1b * 2b)) = 0
(-1ab + 2a2 + (4ab + -2b2)) = 0

Reorder the terms:
(-1ab + 4ab + 2a2 + -2b2) = 0

Combine like terms: -1ab + 4ab = 3ab
(3ab + 2a2 + -2b2) = 0

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

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve:

Simplifying
2a + -1b = 0

Solving
2a + -1b = 0

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

Add 'b' to each side of the equation.
2a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
2a + 0 = 0 + b
2a = 0 + b
Remove the zero:
2a = b

Divide each side by '2'.
a = 0.5b

Simplifying
a = 0.5b

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

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

Simplifying
a = -2b
Solution
a = {0.5b, -2b}

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