(x-5)(2x-3)=4

Solution for (x-5)(2x-3)=4 equation:

Simplifying
(x + -5)(2x + -3) = 4

Reorder the terms:
(-5 + x)(2x + -3) = 4

Reorder the terms:
(-5 + x)(-3 + 2x) = 4

Multiply (-5 + x) * (-3 + 2x)
(-5(-3 + 2x) + x(-3 + 2x)) = 4
((-3 * -5 + 2x * -5) + x(-3 + 2x)) = 4
((15 + -10x) + x(-3 + 2x)) = 4
(15 + -10x + (-3 * x + 2x * x)) = 4
(15 + -10x + (-3x + 2x2)) = 4

Combine like terms: -10x + -3x = -13x
(15 + -13x + 2x2) = 4

Solving
15 + -13x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
15 + -4 + -13x + 2x2 = 4 + -4

Combine like terms: 15 + -4 = 11
11 + -13x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
11 + -13x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -2x) = 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 '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {1, 5.5}