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

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

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

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

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

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

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) = 10x

Solving
6 + 5x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
6 + 5x + -10x + x2 = 10x + -10x

Combine like terms: 5x + -10x = -5x
6 + -5x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
6 + -5x + x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -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 '(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
Solution
x = {2, 3}