4(x+1)=x(x+4)-(x-2)(x+2)

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Solution for 4(x+1)=x(x+4)-(x-2)(x+2) equation:


Simplifying
4(x + 1) = x(x + 4) + -1(x + -2)(x + 2)

Reorder the terms:
4(1 + x) = x(x + 4) + -1(x + -2)(x + 2)
(1 * 4 + x * 4) = x(x + 4) + -1(x + -2)(x + 2)
(4 + 4x) = x(x + 4) + -1(x + -2)(x + 2)

Reorder the terms:
4 + 4x = x(4 + x) + -1(x + -2)(x + 2)
4 + 4x = (4 * x + x * x) + -1(x + -2)(x + 2)
4 + 4x = (4x + x2) + -1(x + -2)(x + 2)

Reorder the terms:
4 + 4x = 4x + x2 + -1(-2 + x)(x + 2)

Reorder the terms:
4 + 4x = 4x + x2 + -1(-2 + x)(2 + x)

Multiply (-2 + x) * (2 + x)
4 + 4x = 4x + x2 + -1(-2(2 + x) + x(2 + x))
4 + 4x = 4x + x2 + -1((2 * -2 + x * -2) + x(2 + x))
4 + 4x = 4x + x2 + -1((-4 + -2x) + x(2 + x))
4 + 4x = 4x + x2 + -1(-4 + -2x + (2 * x + x * x))
4 + 4x = 4x + x2 + -1(-4 + -2x + (2x + x2))

Combine like terms: -2x + 2x = 0
4 + 4x = 4x + x2 + -1(-4 + 0 + x2)
4 + 4x = 4x + x2 + -1(-4 + x2)
4 + 4x = 4x + x2 + (-4 * -1 + x2 * -1)
4 + 4x = 4x + x2 + (4 + -1x2)

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

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

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

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

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

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

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

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

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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