(a-2b)(4a+5b)=

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Solution for (a-2b)(4a+5b)= equation: 


Simplifying
(a + -2b)(4a + 5b) = 0

Multiply (a + -2b) * (4a + 5b)
(a(4a + 5b) + -2b * (4a + 5b)) = 0
((4a * a + 5b * a) + -2b * (4a + 5b)) = 0

Reorder the terms:
((5ab + 4a2) + -2b * (4a + 5b)) = 0
((5ab + 4a2) + -2b * (4a + 5b)) = 0
(5ab + 4a2 + (4a * -2b + 5b * -2b)) = 0
(5ab + 4a2 + (-8ab + -10b2)) = 0

Reorder the terms:
(5ab + -8ab + 4a2 + -10b2) = 0

Combine like terms: 5ab + -8ab = -3ab
(-3ab + 4a2 + -10b2) = 0

Solving
-3ab + 4a2 + -10b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2b)(4a + 5b) = 0


Subproblem 1
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 2
Set the factor '(4a + 5b)' equal to zero and attempt to solve:

Simplifying
4a + 5b = 0

Solving
4a + 5b = 0

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

Add '-5b' to each side of the equation.
4a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
4a + 0 = 0 + -5b
4a = 0 + -5b
Remove the zero:
4a = -5b

Divide each side by '4'.
a = -1.25b

Simplifying
a = -1.25b
Solution
a = {2b, -1.25b}

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