(x-2)(x+2)+3x=(4+x)(x-4)

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Solution for (x-2)(x+2)+3x=(4+x)(x-4) equation:


Simplifying
(x + -2)(x + 2) + 3x = (4 + x)(x + -4)

Reorder the terms:
(-2 + x)(x + 2) + 3x = (4 + x)(x + -4)

Reorder the terms:
(-2 + x)(2 + x) + 3x = (4 + x)(x + -4)

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x)) + 3x = (4 + x)(x + -4)
((2 * -2 + x * -2) + x(2 + x)) + 3x = (4 + x)(x + -4)
((-4 + -2x) + x(2 + x)) + 3x = (4 + x)(x + -4)
(-4 + -2x + (2 * x + x * x)) + 3x = (4 + x)(x + -4)
(-4 + -2x + (2x + x2)) + 3x = (4 + x)(x + -4)

Combine like terms: -2x + 2x = 0
(-4 + 0 + x2) + 3x = (4 + x)(x + -4)
(-4 + x2) + 3x = (4 + x)(x + -4)

Reorder the terms:
-4 + 3x + x2 = (4 + x)(x + -4)

Reorder the terms:
-4 + 3x + x2 = (4 + x)(-4 + x)

Multiply (4 + x) * (-4 + x)
-4 + 3x + x2 = (4(-4 + x) + x(-4 + x))
-4 + 3x + x2 = ((-4 * 4 + x * 4) + x(-4 + x))
-4 + 3x + x2 = ((-16 + 4x) + x(-4 + x))
-4 + 3x + x2 = (-16 + 4x + (-4 * x + x * x))
-4 + 3x + x2 = (-16 + 4x + (-4x + x2))

Combine like terms: 4x + -4x = 0
-4 + 3x + x2 = (-16 + 0 + x2)
-4 + 3x + x2 = (-16 + x2)

Add '-1x2' to each side of the equation.
-4 + 3x + x2 + -1x2 = -16 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x + 0 = -16 + x2 + -1x2
-4 + 3x = -16 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x = -16 + 0
-4 + 3x = -16

Solving
-4 + 3x = -16

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + 3x = -16 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = -16 + 4
3x = -16 + 4

Combine like terms: -16 + 4 = -12
3x = -12

Divide each side by '3'.
x = -4

Simplifying
x = -4

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