8(x-1)(x-2)=4(x^2-4)

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Solution for 8(x-1)(x-2)=4(x^2-4) equation: 


Simplifying
8(x + -1)(x + -2) = 4(x2 + -4)

Reorder the terms:
8(-1 + x)(x + -2) = 4(x2 + -4)

Reorder the terms:
8(-1 + x)(-2 + x) = 4(x2 + -4)

Multiply (-1 + x) * (-2 + x)
8(-1(-2 + x) + x(-2 + x)) = 4(x2 + -4)
8((-2 * -1 + x * -1) + x(-2 + x)) = 4(x2 + -4)
8((2 + -1x) + x(-2 + x)) = 4(x2 + -4)
8(2 + -1x + (-2 * x + x * x)) = 4(x2 + -4)
8(2 + -1x + (-2x + x2)) = 4(x2 + -4)

Combine like terms: -1x + -2x = -3x
8(2 + -3x + x2) = 4(x2 + -4)
(2 * 8 + -3x * 8 + x2 * 8) = 4(x2 + -4)
(16 + -24x + 8x2) = 4(x2 + -4)

Reorder the terms:
16 + -24x + 8x2 = 4(-4 + x2)
16 + -24x + 8x2 = (-4 * 4 + x2 * 4)
16 + -24x + 8x2 = (-16 + 4x2)

Solving
16 + -24x + 8x2 = -16 + 4x2

Solving for variable 'x'.

Reorder the terms:
16 + 16 + -24x + 8x2 + -4x2 = -16 + 4x2 + 16 + -4x2

Combine like terms: 16 + 16 = 32
32 + -24x + 8x2 + -4x2 = -16 + 4x2 + 16 + -4x2

Combine like terms: 8x2 + -4x2 = 4x2
32 + -24x + 4x2 = -16 + 4x2 + 16 + -4x2

Reorder the terms:
32 + -24x + 4x2 = -16 + 16 + 4x2 + -4x2

Combine like terms: -16 + 16 = 0
32 + -24x + 4x2 = 0 + 4x2 + -4x2
32 + -24x + 4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
32 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -6x + x2) = 0

Factor a trinomial.
4((2 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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