4a^2+11ab+6b^2=0

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Solution for 4a^2+11ab+6b^2=0 equation: 


Simplifying
4a2 + 11ab + 6b2 = 0

Reorder the terms:
11ab + 4a2 + 6b2 = 0

Solving
11ab + 4a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + 3b)(a + 2b) = 0


Subproblem 1
Set the factor '(4a + 3b)' equal to zero and attempt to solve:

Simplifying
4a + 3b = 0

Solving
4a + 3b = 0

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

Add '-3b' to each side of the equation.
4a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
4a + 0 = 0 + -3b
4a = 0 + -3b
Remove the zero:
4a = -3b

Divide each side by '4'.
a = -0.75b

Simplifying
a = -0.75b

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 = {-0.75b, -2b}

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