(2x-3)(x-2)=10

Solution for (2x-3)(x-2)=10 equation:

Simplifying
(2x + -3)(x + -2) = 10

Reorder the terms:
(-3 + 2x)(x + -2) = 10

Reorder the terms:
(-3 + 2x)(-2 + x) = 10

Multiply (-3 + 2x) * (-2 + x)
(-3(-2 + x) + 2x * (-2 + x)) = 10
((-2 * -3 + x * -3) + 2x * (-2 + x)) = 10
((6 + -3x) + 2x * (-2 + x)) = 10
(6 + -3x + (-2 * 2x + x * 2x)) = 10
(6 + -3x + (-4x + 2x2)) = 10

Combine like terms: -3x + -4x = -7x
(6 + -7x + 2x2) = 10

Solving
6 + -7x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + -7x + 2x2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + -7x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + -7x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(4 + -1x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.5, 4}