x^2-8x+16=(x-4)(3-2x)

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Solution for x^2-8x+16=(x-4)(3-2x) equation: 


Simplifying
x2 + -8x + 16 = (x + -4)(3 + -2x)

Reorder the terms:
16 + -8x + x2 = (x + -4)(3 + -2x)

Reorder the terms:
16 + -8x + x2 = (-4 + x)(3 + -2x)

Multiply (-4 + x) * (3 + -2x)
16 + -8x + x2 = (-4(3 + -2x) + x(3 + -2x))
16 + -8x + x2 = ((3 * -4 + -2x * -4) + x(3 + -2x))
16 + -8x + x2 = ((-12 + 8x) + x(3 + -2x))
16 + -8x + x2 = (-12 + 8x + (3 * x + -2x * x))
16 + -8x + x2 = (-12 + 8x + (3x + -2x2))

Combine like terms: 8x + 3x = 11x
16 + -8x + x2 = (-12 + 11x + -2x2)

Solving
16 + -8x + x2 = -12 + 11x + -2x2

Solving for variable 'x'.

Reorder the terms:
16 + 12 + -8x + -11x + x2 + 2x2 = -12 + 11x + -2x2 + 12 + -11x + 2x2

Combine like terms: 16 + 12 = 28
28 + -8x + -11x + x2 + 2x2 = -12 + 11x + -2x2 + 12 + -11x + 2x2

Combine like terms: -8x + -11x = -19x
28 + -19x + x2 + 2x2 = -12 + 11x + -2x2 + 12 + -11x + 2x2

Combine like terms: x2 + 2x2 = 3x2
28 + -19x + 3x2 = -12 + 11x + -2x2 + 12 + -11x + 2x2

Reorder the terms:
28 + -19x + 3x2 = -12 + 12 + 11x + -11x + -2x2 + 2x2

Combine like terms: -12 + 12 = 0
28 + -19x + 3x2 = 0 + 11x + -11x + -2x2 + 2x2
28 + -19x + 3x2 = 11x + -11x + -2x2 + 2x2

Combine like terms: 11x + -11x = 0
28 + -19x + 3x2 = 0 + -2x2 + 2x2
28 + -19x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
28 + -19x + 3x2 = 0

Factor a trinomial.
(7 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

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 = {2.333333333, 4}

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