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

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


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

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

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

Multiply (-6 + x) * (-3 + x)
(-6(-3 + x) + x(-3 + x)) = 4
((-3 * -6 + x * -6) + x(-3 + x)) = 4
((18 + -6x) + x(-3 + x)) = 4
(18 + -6x + (-3 * x + x * x)) = 4
(18 + -6x + (-3x + x2)) = 4

Combine like terms: -6x + -3x = -9x
(18 + -9x + x2) = 4

Solving
18 + -9x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
18 + -4 + -9x + x2 = 4 + -4

Combine like terms: 18 + -4 = 14
14 + -9x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
14 + -9x + x2 = 0

Factor a trinomial.
(2 + -1x)(7 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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