2x(x+3)-x(x-5)=26

Solution for 2x(x+3)-x(x-5)=26 equation:

Simplifying
2x(x + 3) + -1x(x + -5) = 26

Reorder the terms:
2x(3 + x) + -1x(x + -5) = 26
(3 * 2x + x * 2x) + -1x(x + -5) = 26
(6x + 2x2) + -1x(x + -5) = 26

Reorder the terms:
6x + 2x2 + -1x(-5 + x) = 26
6x + 2x2 + (-5 * -1x + x * -1x) = 26
6x + 2x2 + (5x + -1x2) = 26

Reorder the terms:
6x + 5x + 2x2 + -1x2 = 26

Combine like terms: 6x + 5x = 11x
11x + 2x2 + -1x2 = 26

Combine like terms: 2x2 + -1x2 = 1x2
11x + 1x2 = 26

Solving
11x + 1x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + 11x + 1x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 11x + 1x2 = 0

Factor a trinomial.
(-13 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
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
Solution
x = {-13, 2}