2x(x-3)=4+x

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

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

Reorder the terms:
2x(-3 + x) = 4 + x
(-3 * 2x + x * 2x) = 4 + x
(-6x + 2x2) = 4 + x

Solving
-6x + 2x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + -1x + 2x2 = 4 + x + -4 + -1x

Combine like terms: -6x + -1x = -7x
-4 + -7x + 2x2 = 4 + x + -4 + -1x

Reorder the terms:
-4 + -7x + 2x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-4 + -7x + 2x2 = 0 + x + -1x
-4 + -7x + 2x2 = x + -1x

Combine like terms: x + -1x = 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}