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

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


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

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

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

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

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

Combine like terms: 4x + -1x = 3x
1x + x2 = (-4 + 3x + x2)

Add '-1x2' to each side of the equation.
1x + x2 + -1x2 = -4 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1x + 0 = -4 + 3x + x2 + -1x2
1x = -4 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1x = -4 + 3x + 0
1x = -4 + 3x

Solving
1x = -4 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
1x + -3x = -4 + 3x + -3x

Combine like terms: 1x + -3x = -2x
-2x = -4 + 3x + -3x

Combine like terms: 3x + -3x = 0
-2x = -4 + 0
-2x = -4

Divide each side by '-2'.
x = 2

Simplifying
x = 2

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