(x-2)(x-5)=4

Solution for (x-2)(x-5)=4 equation:

Simplifying
(x + -2)(x + -5) = 4

Reorder the terms:
(-2 + x)(x + -5) = 4

Reorder the terms:
(-2 + x)(-5 + x) = 4

Multiply (-2 + x) * (-5 + x)
(-2(-5 + x) + x(-5 + x)) = 4
((-5 * -2 + x * -2) + x(-5 + x)) = 4
((10 + -2x) + x(-5 + x)) = 4
(10 + -2x + (-5 * x + x * x)) = 4
(10 + -2x + (-5x + x2)) = 4

Combine like terms: -2x + -5x = -7x
(10 + -7x + x2) = 4

Solving
10 + -7x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
10 + -4 + -7x + x2 = 4 + -4

Combine like terms: 10 + -4 = 6
6 + -7x + x2 = 4 + -4

Combine like terms: 4 + -4 = 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}