2a^2+7ab-15b^2=0

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Solution for 2a^2+7ab-15b^2=0 equation: 


Simplifying
2a2 + 7ab + -15b2 = 0

Reorder the terms:
7ab + 2a2 + -15b2 = 0

Solving
7ab + 2a2 + -15b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(a + 5b) = 0


Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b

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

Simplifying
a + 5b = 0

Solving
a + 5b = 0

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

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

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

Simplifying
a = -5b
Solution
a = {1.5b, -5b}

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