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

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


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

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

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

Reorder the terms:
(20ab + -2ab + 2a2 + -20b2) = 0

Combine like terms: 20ab + -2ab = 18ab
(18ab + 2a2 + -20b2) = 0

Solving
18ab + 2a2 + -20b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9ab + a2 + -10b2) = 0

Factor a trinomial.
2((a + -1b)(a + 10b)) = 0

Ignore the factor 2.

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

Simplifying
a = b

Subproblem 2
Set the factor '(a + 10b)' equal to zero and attempt to solve:

Simplifying
a + 10b = 0

Solving
a + 10b = 0

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

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

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

Simplifying
a = -10b
Solution
a = {b, -10b}

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