2x(x-4)=x+5

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

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

Reorder the terms:
2x(-4 + x) = x + 5
(-4 * 2x + x * 2x) = x + 5
(-8x + 2x2) = x + 5

Reorder the terms:
-8x + 2x2 = 5 + x

Solving
-8x + 2x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + -8x + -1x + 2x2 = 5 + x + -5 + -1x

Combine like terms: -8x + -1x = -9x
-5 + -9x + 2x2 = 5 + x + -5 + -1x

Reorder the terms:
-5 + -9x + 2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-5 + -9x + 2x2 = 0 + x + -1x
-5 + -9x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -9x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.5, 5}