4x^2+5bx=-b^2

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Solution for 4x^2+5bx=-b^2 equation: 


Simplifying
4x2 + 5bx = -1b2

Reorder the terms:
5bx + 4x2 = -1b2

Solving
5bx + 4x2 = -1b2

Solving for variable 'b'.

Reorder the terms:
5bx + b2 + 4x2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
5bx + b2 + 4x2 = 0

Factor a trinomial.
(b + x)(b + 4x) = 0


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

Simplifying
b + x = 0

Solving
b + x = 0

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

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

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

Simplifying
b = -1x

Subproblem 2
Set the factor '(b + 4x)' equal to zero and attempt to solve:

Simplifying
b + 4x = 0

Solving
b + 4x = 0

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

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

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

Simplifying
b = -4x
Solution
b = {-1x, -4x}

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