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

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

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

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

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

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

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

Combine like terms: 4 + 1 = 5
-4 + 7x + 2x2 = 5

Solving
-4 + 7x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-4 + -5 + 7x + 2x2 = 5 + -5

Combine like terms: -4 + -5 = -9
-9 + 7x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-9 + 7x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
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 = {-4.5, 1}