(3-X)*(4-X)=6

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Solution for (3-X)*(4-X)=6 equation:


Simplifying
(3 + -1X)(4 + -1X) = 6

Multiply (3 + -1X) * (4 + -1X)
(3(4 + -1X) + -1X * (4 + -1X)) = 6
((4 * 3 + -1X * 3) + -1X * (4 + -1X)) = 6
((12 + -3X) + -1X * (4 + -1X)) = 6
(12 + -3X + (4 * -1X + -1X * -1X)) = 6
(12 + -3X + (-4X + 1X2)) = 6

Combine like terms: -3X + -4X = -7X
(12 + -7X + 1X2) = 6

Solving
12 + -7X + 1X2 = 6

Solving for variable 'X'.

Reorder the terms:
12 + -6 + -7X + 1X2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + -7X + 1X2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + -7X + 1X2 = 0

Factor a trinomial.
(1 + -1X)(6 + -1X) = 0

Subproblem 1

Set the factor '(1 + -1X)' equal to zero and attempt to solve: Simplifying 1 + -1X = 0 Solving 1 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1X = 0 + -1 -1X = 0 + -1 Combine like terms: 0 + -1 = -1 -1X = -1 Divide each side by '-1'. X = 1 Simplifying X = 1

Subproblem 2

Set the factor '(6 + -1X)' equal to zero and attempt to solve: Simplifying 6 + -1X = 0 Solving 6 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1X = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1X = 0 + -6 -1X = 0 + -6 Combine like terms: 0 + -6 = -6 -1X = -6 Divide each side by '-1'. X = 6 Simplifying X = 6

Solution

X = {1, 6}

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