(x-6)(x-3)=10

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Solution for (x-6)(x-3)=10 equation:


Simplifying
(x + -6)(x + -3) = 10

Reorder the terms:
(-6 + x)(x + -3) = 10

Reorder the terms:
(-6 + x)(-3 + x) = 10

Multiply (-6 + x) * (-3 + x)
(-6(-3 + x) + x(-3 + x)) = 10
((-3 * -6 + x * -6) + x(-3 + x)) = 10
((18 + -6x) + x(-3 + x)) = 10
(18 + -6x + (-3 * x + x * x)) = 10
(18 + -6x + (-3x + x2)) = 10

Combine like terms: -6x + -3x = -9x
(18 + -9x + x2) = 10

Solving
18 + -9x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
18 + -10 + -9x + x2 = 10 + -10

Combine like terms: 18 + -10 = 8
8 + -9x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
8 + -9x + x2 = 0

Factor a trinomial.
(1 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {1, 8}

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