6x=(x-1)(x+4)

Solution for 6x=(x-1)(x+4) equation:

Simplifying
6x = (x + -1)(x + 4)

Reorder the terms:
6x = (-1 + x)(x + 4)

Reorder the terms:
6x = (-1 + x)(4 + x)

Multiply (-1 + x) * (4 + x)
6x = (-1(4 + x) + x(4 + x))
6x = ((4 * -1 + x * -1) + x(4 + x))
6x = ((-4 + -1x) + x(4 + x))
6x = (-4 + -1x + (4 * x + x * x))
6x = (-4 + -1x + (4x + x2))

Combine like terms: -1x + 4x = 3x
6x = (-4 + 3x + x2)

Solving
6x = -4 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
4 + 6x + -3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: 6x + -3x = 3x
4 + 3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Reorder the terms:
4 + 3x + -1x2 = -4 + 4 + 3x + -3x + x2 + -1x2

Combine like terms: -4 + 4 = 0
4 + 3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
4 + 3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
4 + 3x + -1x2 = 0 + x2 + -1x2
4 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 3x + -1x2 = 0

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

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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