10a^2-23ab-5b^2=

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Solution for 10a^2-23ab-5b^2= equation: 


Simplifying
10a2 + -23ab + -5b2 = 0

Reorder the terms:
-23ab + 10a2 + -5b2 = 0

Solving
-23ab + 10a2 + -5b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -5b)(5a + b) = 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 '(5a + b)' equal to zero and attempt to solve:

Simplifying
5a + b = 0

Solving
5a + b = 0

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

Add '-1b' to each side of the equation.
5a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
5a + 0 = 0 + -1b
5a = 0 + -1b
Remove the zero:
5a = -1b

Divide each side by '5'.
a = -0.2b

Simplifying
a = -0.2b
Solution
a = {2.5b, -0.2b}

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