4x^2+12wx+5w^2=0

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Solution for 4x^2+12wx+5w^2=0 equation: 


Simplifying
4x2 + 12wx + 5w2 = 0

Reorder the terms:
12wx + 5w2 + 4x2 = 0

Solving
12wx + 5w2 + 4x2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5w + 2x)(w + 2x) = 0


Subproblem 1
Set the factor '(5w + 2x)' equal to zero and attempt to solve:

Simplifying
5w + 2x = 0

Solving
5w + 2x = 0

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

Add '-2x' to each side of the equation.
5w + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
5w + 0 = 0 + -2x
5w = 0 + -2x
Remove the zero:
5w = -2x

Divide each side by '5'.
w = -0.4x

Simplifying
w = -0.4x

Subproblem 2
Set the factor '(w + 2x)' equal to zero and attempt to solve:

Simplifying
w + 2x = 0

Solving
w + 2x = 0

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

Add '-2x' to each side of the equation.
w + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
w + 0 = 0 + -2x
w = 0 + -2x
Remove the zero:
w = -2x

Simplifying
w = -2x
Solution
w = {-0.4x, -2x}

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