X^2-5x^2+4x=0

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Solution for X^2-5x^2+4x=0 equation: 


Simplifying
X2 + -5x2 + 4x = 0

Reorder the terms:
X2 + 4x + -5x2 = 0

Solving
X2 + 4x + -5x2 = 0

Solving for variable 'X'.

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

Add '-4x' to each side of the equation.
X2 + 4x + -4x + -5x2 = 0 + -4x

Combine like terms: 4x + -4x = 0
X2 + 0 + -5x2 = 0 + -4x
X2 + -5x2 = 0 + -4x
Remove the zero:
X2 + -5x2 = -4x

Add '5x2' to each side of the equation.
X2 + -5x2 + 5x2 = -4x + 5x2

Combine like terms: -5x2 + 5x2 = 0
X2 + 0 = -4x + 5x2
X2 = -4x + 5x2

Simplifying
X2 = -4x + 5x2

Reorder the terms:
X2 + 4x + -5x2 = -4x + 4x + 5x2 + -5x2

Combine like terms: -4x + 4x = 0
X2 + 4x + -5x2 = 0 + 5x2 + -5x2
X2 + 4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
X2 + 4x + -5x2 = 0

Factor a trinomial.
(X + -1x)(X + 5x) = 0


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

Simplifying
X + -1x = 0

Solving
X + -1x = 0

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

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

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

Simplifying
X = x

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

Simplifying
X + 5x = 0

Solving
X + 5x = 0

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

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

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

Simplifying
X = -5x
Solution
X = {x, -5x}

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