50=(9-2x)(12-x)

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Solution for 50=(9-2x)(12-x) equation: 


Simplifying
50 = (9 + -2x)(12 + -1x)

Multiply (9 + -2x) * (12 + -1x)
50 = (9(12 + -1x) + -2x * (12 + -1x))
50 = ((12 * 9 + -1x * 9) + -2x * (12 + -1x))
50 = ((108 + -9x) + -2x * (12 + -1x))
50 = (108 + -9x + (12 * -2x + -1x * -2x))
50 = (108 + -9x + (-24x + 2x2))

Combine like terms: -9x + -24x = -33x
50 = (108 + -33x + 2x2)

Solving
50 = 108 + -33x + 2x2

Solving for variable 'x'.

Combine like terms: 50 + -108 = -58
-58 + 33x + -2x2 = 108 + -33x + 2x2 + -108 + 33x + -2x2

Reorder the terms:
-58 + 33x + -2x2 = 108 + -108 + -33x + 33x + 2x2 + -2x2

Combine like terms: 108 + -108 = 0
-58 + 33x + -2x2 = 0 + -33x + 33x + 2x2 + -2x2
-58 + 33x + -2x2 = -33x + 33x + 2x2 + -2x2

Combine like terms: -33x + 33x = 0
-58 + 33x + -2x2 = 0 + 2x2 + -2x2
-58 + 33x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-58 + 33x + -2x2 = 0

Factor a trinomial.
(-29 + 2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-29 + 2x)' equal to zero and attempt to solve:

Simplifying
-29 + 2x = 0

Solving
-29 + 2x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 2x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 2x = 0 + 29
2x = 0 + 29

Combine like terms: 0 + 29 = 29
2x = 29

Divide each side by '2'.
x = 14.5

Simplifying
x = 14.5

Subproblem 2
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
Solution
x = {14.5, 2}

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