(x-9)(x-4)=6

Solution for (x-9)(x-4)=6 equation:

Simplifying
(x + -9)(x + -4) = 6

Reorder the terms:
(-9 + x)(x + -4) = 6

Reorder the terms:
(-9 + x)(-4 + x) = 6

Multiply (-9 + x) * (-4 + x)
(-9(-4 + x) + x(-4 + x)) = 6
((-4 * -9 + x * -9) + x(-4 + x)) = 6
((36 + -9x) + x(-4 + x)) = 6
(36 + -9x + (-4 * x + x * x)) = 6
(36 + -9x + (-4x + x2)) = 6

Combine like terms: -9x + -4x = -13x
(36 + -13x + x2) = 6

Solving
36 + -13x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
36 + -6 + -13x + x2 = 6 + -6

Combine like terms: 36 + -6 = 30
30 + -13x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
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 = {3, 10}