2x^2-8x+2=(x-2)(x-3)

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Solution for 2x^2-8x+2=(x-2)(x-3) equation: 


Simplifying
2x2 + -8x + 2 = (x + -2)(x + -3)

Reorder the terms:
2 + -8x + 2x2 = (x + -2)(x + -3)

Reorder the terms:
2 + -8x + 2x2 = (-2 + x)(x + -3)

Reorder the terms:
2 + -8x + 2x2 = (-2 + x)(-3 + x)

Multiply (-2 + x) * (-3 + x)
2 + -8x + 2x2 = (-2(-3 + x) + x(-3 + x))
2 + -8x + 2x2 = ((-3 * -2 + x * -2) + x(-3 + x))
2 + -8x + 2x2 = ((6 + -2x) + x(-3 + x))
2 + -8x + 2x2 = (6 + -2x + (-3 * x + x * x))
2 + -8x + 2x2 = (6 + -2x + (-3x + x2))

Combine like terms: -2x + -3x = -5x
2 + -8x + 2x2 = (6 + -5x + x2)

Solving
2 + -8x + 2x2 = 6 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
2 + -6 + -8x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 2 + -6 = -4
-4 + -8x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: -8x + 5x = -3x
-4 + -3x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + -3x + 1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Reorder the terms:
-4 + -3x + 1x2 = 6 + -6 + -5x + 5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-4 + -3x + 1x2 = 0 + -5x + 5x + x2 + -1x2
-4 + -3x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-4 + -3x + 1x2 = 0 + x2 + -1x2
-4 + -3x + 1x2 = x2 + -1x2

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

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


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

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 = {-1, 4}

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