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

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

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

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

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

Add '-6' to each side of the equation.
6 + -6 + 36x = 6 + -1x + -6 + 4x2

Combine like terms: 6 + -6 = 0
0 + 36x = 6 + -1x + -6 + 4x2
36x = 6 + -1x + -6 + 4x2

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

Combine like terms: 6 + -6 = 0
36x = 0 + -1x + 4x2
36x = -1x + 4x2

Solving
36x = -1x + 4x2

Solving for variable 'x'.

Combine like terms: 36x + x = 37x
37x + -4x2 = -1x + 4x2 + x + -4x2

Reorder the terms:
37x + -4x2 = -1x + x + 4x2 + -4x2

Combine like terms: -1x + x = 0
37x + -4x2 = 0 + 4x2 + -4x2
37x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
37x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(37 + -4x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(37 + -4x)' equal to zero and attempt to solve:

Simplifying
37 + -4x = 0

Solving
37 + -4x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -4x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -4x = 0 + -37
-4x = 0 + -37

Combine like terms: 0 + -37 = -37
-4x = -37

Divide each side by '-4'.
x = 9.25

Simplifying
x = 9.25
Solution
x = {0, 9.25}