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

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


Simplifying
(2a + b) * x(a + -2b) = 0

Reorder the terms for easier multiplication:
x(2a + b)(a + -2b) = 0

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

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

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

Combine like terms: -4ab + ab = -3ab
x(-3ab + 2a2 + -2b2) = 0
(-3ab * x + 2a2 * x + -2b2 * x) = 0
(-3abx + 2a2x + -2b2x) = 0

Solving
-3abx + 2a2x + -2b2x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3ab + 2a2 + -2b2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

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

Simplifying
2a + b = 0

Solving
2a + b = 0

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

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

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

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

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

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