(2x-1)(x+4)=4+x

Solution for (2x-1)(x+4)=4+x equation:

Simplifying
(2x + -1)(x + 4) = 4 + x

Reorder the terms:
(-1 + 2x)(x + 4) = 4 + x

Reorder the terms:
(-1 + 2x)(4 + x) = 4 + x

Multiply (-1 + 2x) * (4 + x)
(-1(4 + x) + 2x * (4 + x)) = 4 + x
((4 * -1 + x * -1) + 2x * (4 + x)) = 4 + x
((-4 + -1x) + 2x * (4 + x)) = 4 + x
(-4 + -1x + (4 * 2x + x * 2x)) = 4 + x
(-4 + -1x + (8x + 2x2)) = 4 + x

Combine like terms: -1x + 8x = 7x
(-4 + 7x + 2x2) = 4 + x

Solving
-4 + 7x + 2x2 = 4 + x

Solving for variable 'x'.

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

Combine like terms: -4 + -4 = -8
-8 + 7x + -1x + 2x2 = 4 + x + -4 + -1x

Combine like terms: 7x + -1x = 6x
-8 + 6x + 2x2 = 4 + x + -4 + -1x

Reorder the terms:
-8 + 6x + 2x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-8 + 6x + 2x2 = 0 + x + -1x
-8 + 6x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3x + x2) = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}