(7-2X)(11-3X)=2

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Solution for (7-2X)(11-3X)=2 equation: 


Simplifying
(7 + -2X)(11 + -3X) = 2

Multiply (7 + -2X) * (11 + -3X)
(7(11 + -3X) + -2X * (11 + -3X)) = 2
((11 * 7 + -3X * 7) + -2X * (11 + -3X)) = 2
((77 + -21X) + -2X * (11 + -3X)) = 2
(77 + -21X + (11 * -2X + -3X * -2X)) = 2
(77 + -21X + (-22X + 6X2)) = 2

Combine like terms: -21X + -22X = -43X
(77 + -43X + 6X2) = 2

Solving
77 + -43X + 6X2 = 2

Solving for variable 'X'.

Reorder the terms:
77 + -2 + -43X + 6X2 = 2 + -2

Combine like terms: 77 + -2 = 75
75 + -43X + 6X2 = 2 + -2

Combine like terms: 2 + -2 = 0
75 + -43X + 6X2 = 0

Factor a trinomial.
(3 + -1X)(25 + -6X) = 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 '(25 + -6X)' equal to zero and attempt to solve:

Simplifying
25 + -6X = 0

Solving
25 + -6X = 0

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

Add '-25' to each side of the equation.
25 + -25 + -6X = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -6X = 0 + -25
-6X = 0 + -25

Combine like terms: 0 + -25 = -25
-6X = -25

Divide each side by '-6'.
X = 4.166666667

Simplifying
X = 4.166666667
Solution
X = {3, 4.166666667}

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