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

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


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

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

Reorder the terms:
((4ab + 2a2) + -5b * (a + 2b)) = 0
((4ab + 2a2) + -5b * (a + 2b)) = 0
(4ab + 2a2 + (a * -5b + 2b * -5b)) = 0
(4ab + 2a2 + (-5ab + -10b2)) = 0

Reorder the terms:
(4ab + -5ab + 2a2 + -10b2) = 0

Combine like terms: 4ab + -5ab = -1ab
(-1ab + 2a2 + -10b2) = 0

Solving
-1ab + 2a2 + -10b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -5b)(a + 2b) = 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 + 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 = {2.5b, -2b}

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