(9a-10b)(2a+b)=

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Solution for (9a-10b)(2a+b)= equation: 


Simplifying
(9a + -10b)(2a + b) = 0

Multiply (9a + -10b) * (2a + b)
(9a * (2a + b) + -10b * (2a + b)) = 0
((2a * 9a + b * 9a) + -10b * (2a + b)) = 0

Reorder the terms:
((9ab + 18a2) + -10b * (2a + b)) = 0
((9ab + 18a2) + -10b * (2a + b)) = 0
(9ab + 18a2 + (2a * -10b + b * -10b)) = 0
(9ab + 18a2 + (-20ab + -10b2)) = 0

Reorder the terms:
(9ab + -20ab + 18a2 + -10b2) = 0

Combine like terms: 9ab + -20ab = -11ab
(-11ab + 18a2 + -10b2) = 0

Solving
-11ab + 18a2 + -10b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9a + -10b)(2a + b) = 0


Subproblem 1
Set the factor '(9a + -10b)' equal to zero and attempt to solve:

Simplifying
9a + -10b = 0

Solving
9a + -10b = 0

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

Add '10b' to each side of the equation.
9a + -10b + 10b = 0 + 10b

Combine like terms: -10b + 10b = 0
9a + 0 = 0 + 10b
9a = 0 + 10b
Remove the zero:
9a = 10b

Divide each side by '9'.
a = 1.111111111b

Simplifying
a = 1.111111111b

Subproblem 2
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 = {1.111111111b, -0.5b}

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