4(x+9)+x(x-1)=x(6+x)

Solution for 4(x+9)+x(x-1)=x(6+x) equation:

Simplifying
4(x + 9) + x(x + -1) = x(6 + x)

Reorder the terms:
4(9 + x) + x(x + -1) = x(6 + x)
(9 * 4 + x * 4) + x(x + -1) = x(6 + x)
(36 + 4x) + x(x + -1) = x(6 + x)

Reorder the terms:
36 + 4x + x(-1 + x) = x(6 + x)
36 + 4x + (-1 * x + x * x) = x(6 + x)
36 + 4x + (-1x + x2) = x(6 + x)

Combine like terms: 4x + -1x = 3x
36 + 3x + x2 = x(6 + x)
36 + 3x + x2 = (6 * x + x * x)
36 + 3x + x2 = (6x + x2)

Add '-1x2' to each side of the equation.
36 + 3x + x2 + -1x2 = 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + 3x + 0 = 6x + x2 + -1x2
36 + 3x = 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + 3x = 6x + 0
36 + 3x = 6x

Solving
36 + 3x = 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
36 + 3x + -6x = 6x + -6x

Combine like terms: 3x + -6x = -3x
36 + -3x = 6x + -6x

Combine like terms: 6x + -6x = 0
36 + -3x = 0

Add '-36' to each side of the equation.
36 + -36 + -3x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -3x = 0 + -36
-3x = 0 + -36

Combine like terms: 0 + -36 = -36
-3x = -36

Divide each side by '-3'.
x = 12

Simplifying
x = 12