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

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


Simplifying
x(2 + -1x) = 3(x + -4)
(2 * x + -1x * x) = 3(x + -4)
(2x + -1x2) = 3(x + -4)

Reorder the terms:
2x + -1x2 = 3(-4 + x)
2x + -1x2 = (-4 * 3 + x * 3)
2x + -1x2 = (-12 + 3x)

Solving
2x + -1x2 = -12 + 3x

Solving for variable 'x'.

Reorder the terms:
12 + 2x + -3x + -1x2 = -12 + 3x + 12 + -3x

Combine like terms: 2x + -3x = -1x
12 + -1x + -1x2 = -12 + 3x + 12 + -3x

Reorder the terms:
12 + -1x + -1x2 = -12 + 12 + 3x + -3x

Combine like terms: -12 + 12 = 0
12 + -1x + -1x2 = 0 + 3x + -3x
12 + -1x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -1x + -1x2 = 0

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {3, -4}

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