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

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

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

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

Reorder the terms:
6 + 1x + 6x2 = 6(1 + 4x)
6 + 1x + 6x2 = (1 * 6 + 4x * 6)
6 + 1x + 6x2 = (6 + 24x)

Add '-6' to each side of the equation.
6 + 1x + -6 + 6x2 = 6 + -6 + 24x

Reorder the terms:
6 + -6 + 1x + 6x2 = 6 + -6 + 24x

Combine like terms: 6 + -6 = 0
0 + 1x + 6x2 = 6 + -6 + 24x
1x + 6x2 = 6 + -6 + 24x

Combine like terms: 6 + -6 = 0
1x + 6x2 = 0 + 24x
1x + 6x2 = 24x

Solving
1x + 6x2 = 24x

Solving for variable 'x'.

Reorder the terms:
1x + -24x + 6x2 = 24x + -24x

Combine like terms: 1x + -24x = -23x
-23x + 6x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-23x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-23 + 6x) = 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 '(-23 + 6x)' equal to zero and attempt to solve:

Simplifying
-23 + 6x = 0

Solving
-23 + 6x = 0

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

Add '23' to each side of the equation.
-23 + 23 + 6x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 6x = 0 + 23
6x = 0 + 23

Combine like terms: 0 + 23 = 23
6x = 23

Divide each side by '6'.
x = 3.833333333

Simplifying
x = 3.833333333
Solution
x = {0, 3.833333333}