5a^2+9ab+4b^2=

Solution for 5a^2+9ab+4b^2= equation:

Simplifying
5a2 + 9ab + 4b2 = 0

Reorder the terms:
9ab + 5a2 + 4b2 = 0

Solving
9ab + 5a2 + 4b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + 4b)(a + b) = 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 '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {-0.8b, -1b}