(x+4)x=(x-5)(x-1)

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Solution for (x+4)x=(x-5)(x-1) equation:


Simplifying
(x + 4) * x = (x + -5)(x + -1)

Reorder the terms:
(4 + x) * x = (x + -5)(x + -1)

Reorder the terms for easier multiplication:
x(4 + x) = (x + -5)(x + -1)
(4 * x + x * x) = (x + -5)(x + -1)
(4x + x2) = (x + -5)(x + -1)

Reorder the terms:
4x + x2 = (-5 + x)(x + -1)

Reorder the terms:
4x + x2 = (-5 + x)(-1 + x)

Multiply (-5 + x) * (-1 + x)
4x + x2 = (-5(-1 + x) + x(-1 + x))
4x + x2 = ((-1 * -5 + x * -5) + x(-1 + x))
4x + x2 = ((5 + -5x) + x(-1 + x))
4x + x2 = (5 + -5x + (-1 * x + x * x))
4x + x2 = (5 + -5x + (-1x + x2))

Combine like terms: -5x + -1x = -6x
4x + x2 = (5 + -6x + x2)

Add '-1x2' to each side of the equation.
4x + x2 + -1x2 = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4x + 0 = 5 + -6x + x2 + -1x2
4x = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4x = 5 + -6x + 0
4x = 5 + -6x

Solving
4x = 5 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
4x + 6x = 5 + -6x + 6x

Combine like terms: 4x + 6x = 10x
10x = 5 + -6x + 6x

Combine like terms: -6x + 6x = 0
10x = 5 + 0
10x = 5

Divide each side by '10'.
x = 0.5

Simplifying
x = 0.5

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