(x-3)(x-4)=6

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Solution for (x-3)(x-4)=6 equation:


Simplifying
(x + -3)(x + -4) = 6

Reorder the terms:
(-3 + x)(x + -4) = 6

Reorder the terms:
(-3 + x)(-4 + x) = 6

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) = 6
((-4 * -3 + x * -3) + x(-4 + x)) = 6
((12 + -3x) + x(-4 + x)) = 6
(12 + -3x + (-4 * x + x * x)) = 6
(12 + -3x + (-4x + x2)) = 6

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) = 6

Solving
12 + -7x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
12 + -6 + -7x + x2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + -7x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + -7x + x2 = 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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