2a^2+7ab+6b^2=0

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Solution for 2a^2+7ab+6b^2=0 equation: 


Simplifying
2a2 + 7ab + 6b2 = 0

Reorder the terms:
7ab + 2a2 + 6b2 = 0

Solving
7ab + 2a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + 3b)(a + 2b) = 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 + 2b)' equal to zero and attempt to solve:

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

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

Simplifying
a = -2b
Solution
a = {-1.5b, -2b}

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