(x-7)(x-8)=6

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Solution for (x-7)(x-8)=6 equation: 


Simplifying
(x + -7)(x + -8) = 6

Reorder the terms:
(-7 + x)(x + -8) = 6

Reorder the terms:
(-7 + x)(-8 + x) = 6

Multiply (-7 + x) * (-8 + x)
(-7(-8 + x) + x(-8 + x)) = 6
((-8 * -7 + x * -7) + x(-8 + x)) = 6
((56 + -7x) + x(-8 + x)) = 6
(56 + -7x + (-8 * x + x * x)) = 6
(56 + -7x + (-8x + x2)) = 6

Combine like terms: -7x + -8x = -15x
(56 + -15x + x2) = 6

Solving
56 + -15x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
56 + -6 + -15x + x2 = 6 + -6

Combine like terms: 56 + -6 = 50
50 + -15x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
50 + -15x + x2 = 0

Factor a trinomial.
(5 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {5, 10}

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