2(3(4+x)x)+x=51

Solution for 2(3(4+x)x)+x=51 equation:

Simplifying
2(3(4 + x) * x) + x = 51

Reorder the terms for easier multiplication:
2(3x(4 + x)) + x = 51
2((4 * 3x + x * 3x)) + x = 51
2((12x + 3x2)) + x = 51
(12x * 2 + 3x2 * 2) + x = 51
(24x + 6x2) + x = 51

Reorder the terms:
24x + x + 6x2 = 51

Combine like terms: 24x + x = 25x
25x + 6x2 = 51

Solving
25x + 6x2 = 51

Solving for variable 'x'.

Reorder the terms:
-51 + 25x + 6x2 = 51 + -51

Combine like terms: 51 + -51 = 0
-51 + 25x + 6x2 = 0

Factor a trinomial.
(-17 + -3x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-17 + -3x)' equal to zero and attempt to solve:

Simplifying
-17 + -3x = 0

Solving
-17 + -3x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -3x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3x = 0 + 17
-3x = 0 + 17

Combine like terms: 0 + 17 = 17
-3x = 17

Divide each side by '-3'.
x = -5.666666667

Simplifying
x = -5.666666667
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-5.666666667, 1.5}