4(x-2)(x-2)=(x-5)(x-4)(x+4)

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Solution for 4(x-2)(x-2)=(x-5)(x-4)(x+4) equation: 


Simplifying
4(x + -2)(x + -2) = (x + -5)(x + -4)(x + 4)

Reorder the terms:
4(-2 + x)(x + -2) = (x + -5)(x + -4)(x + 4)

Reorder the terms:
4(-2 + x)(-2 + x) = (x + -5)(x + -4)(x + 4)

Multiply (-2 + x) * (-2 + x)
4(-2(-2 + x) + x(-2 + x)) = (x + -5)(x + -4)(x + 4)
4((-2 * -2 + x * -2) + x(-2 + x)) = (x + -5)(x + -4)(x + 4)
4((4 + -2x) + x(-2 + x)) = (x + -5)(x + -4)(x + 4)
4(4 + -2x + (-2 * x + x * x)) = (x + -5)(x + -4)(x + 4)
4(4 + -2x + (-2x + x2)) = (x + -5)(x + -4)(x + 4)

Combine like terms: -2x + -2x = -4x
4(4 + -4x + x2) = (x + -5)(x + -4)(x + 4)
(4 * 4 + -4x * 4 + x2 * 4) = (x + -5)(x + -4)(x + 4)
(16 + -16x + 4x2) = (x + -5)(x + -4)(x + 4)

Reorder the terms:
16 + -16x + 4x2 = (-5 + x)(x + -4)(x + 4)

Reorder the terms:
16 + -16x + 4x2 = (-5 + x)(-4 + x)(x + 4)

Reorder the terms:
16 + -16x + 4x2 = (-5 + x)(-4 + x)(4 + x)

Multiply (-5 + x) * (-4 + x)
16 + -16x + 4x2 = (-5(-4 + x) + x(-4 + x))(4 + x)
16 + -16x + 4x2 = ((-4 * -5 + x * -5) + x(-4 + x))(4 + x)
16 + -16x + 4x2 = ((20 + -5x) + x(-4 + x))(4 + x)
16 + -16x + 4x2 = (20 + -5x + (-4 * x + x * x))(4 + x)
16 + -16x + 4x2 = (20 + -5x + (-4x + x2))(4 + x)

Combine like terms: -5x + -4x = -9x
16 + -16x + 4x2 = (20 + -9x + x2)(4 + x)

Multiply (20 + -9x + x2) * (4 + x)
16 + -16x + 4x2 = (20(4 + x) + -9x * (4 + x) + x2(4 + x))
16 + -16x + 4x2 = ((4 * 20 + x * 20) + -9x * (4 + x) + x2(4 + x))
16 + -16x + 4x2 = ((80 + 20x) + -9x * (4 + x) + x2(4 + x))
16 + -16x + 4x2 = (80 + 20x + (4 * -9x + x * -9x) + x2(4 + x))
16 + -16x + 4x2 = (80 + 20x + (-36x + -9x2) + x2(4 + x))
16 + -16x + 4x2 = (80 + 20x + -36x + -9x2 + (4 * x2 + x * x2))
16 + -16x + 4x2 = (80 + 20x + -36x + -9x2 + (4x2 + x3))

Combine like terms: 20x + -36x = -16x
16 + -16x + 4x2 = (80 + -16x + -9x2 + 4x2 + x3)

Combine like terms: -9x2 + 4x2 = -5x2
16 + -16x + 4x2 = (80 + -16x + -5x2 + x3)

Add '16x' to each side of the equation.
16 + -16x + 16x + 4x2 = 80 + -16x + -5x2 + 16x + x3

Combine like terms: -16x + 16x = 0
16 + 0 + 4x2 = 80 + -16x + -5x2 + 16x + x3
16 + 4x2 = 80 + -16x + -5x2 + 16x + x3

Reorder the terms:
16 + 4x2 = 80 + -16x + 16x + -5x2 + x3

Combine like terms: -16x + 16x = 0
16 + 4x2 = 80 + 0 + -5x2 + x3
16 + 4x2 = 80 + -5x2 + x3

Solving
16 + 4x2 = 80 + -5x2 + x3

Solving for variable 'x'.

Reorder the terms:
16 + -80 + 4x2 + 5x2 + -1x3 = 80 + -5x2 + x3 + -80 + 5x2 + -1x3

Combine like terms: 16 + -80 = -64
-64 + 4x2 + 5x2 + -1x3 = 80 + -5x2 + x3 + -80 + 5x2 + -1x3

Combine like terms: 4x2 + 5x2 = 9x2
-64 + 9x2 + -1x3 = 80 + -5x2 + x3 + -80 + 5x2 + -1x3

Reorder the terms:
-64 + 9x2 + -1x3 = 80 + -80 + -5x2 + 5x2 + x3 + -1x3

Combine like terms: 80 + -80 = 0
-64 + 9x2 + -1x3 = 0 + -5x2 + 5x2 + x3 + -1x3
-64 + 9x2 + -1x3 = -5x2 + 5x2 + x3 + -1x3

Combine like terms: -5x2 + 5x2 = 0
-64 + 9x2 + -1x3 = 0 + x3 + -1x3
-64 + 9x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-64 + 9x2 + -1x3 = 0

The solution to this equation could not be determined.

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