10a^2+17ab-20b^2=0

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Solution for 10a^2+17ab-20b^2=0 equation: 


Simplifying
10a2 + 17ab + -20b2 = 0

Reorder the terms:
17ab + 10a2 + -20b2 = 0

Solving
17ab + 10a2 + -20b2 = 0

Solving for variable 'a'.

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


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

Simplifying
5a + -4b = 0

Solving
5a + -4b = 0

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

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

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

Divide each side by '5'.
a = 0.8b

Simplifying
a = 0.8b

Subproblem 2
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
Solution
a = {0.8b, -2.5b}

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