(5-2x)(4-x)=2

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Solution for (5-2x)(4-x)=2 equation: 


Simplifying
(5 + -2x)(4 + -1x) = 2

Multiply (5 + -2x) * (4 + -1x)
(5(4 + -1x) + -2x * (4 + -1x)) = 2
((4 * 5 + -1x * 5) + -2x * (4 + -1x)) = 2
((20 + -5x) + -2x * (4 + -1x)) = 2
(20 + -5x + (4 * -2x + -1x * -2x)) = 2
(20 + -5x + (-8x + 2x2)) = 2

Combine like terms: -5x + -8x = -13x
(20 + -13x + 2x2) = 2

Solving
20 + -13x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
20 + -2 + -13x + 2x2 = 2 + -2

Combine like terms: 20 + -2 = 18
18 + -13x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
18 + -13x + 2x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -2x) = 0


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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {2, 4.5}

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