5[3(x+4)(1-x)]-x-25=14x+55

Solution for 5[3(x+4)(1-x)]-x-25=14x+55 equation:

Simplifying
5[3(x + 4)(1 + -1x)] + -1x + -25 = 14x + 55

Reorder the terms:
5[3(4 + x)(1 + -1x)] + -1x + -25 = 14x + 55

Multiply (4 + x) * (1 + -1x)
5[3(4(1 + -1x) + x(1 + -1x))] + -1x + -25 = 14x + 55
5[3((1 * 4 + -1x * 4) + x(1 + -1x))] + -1x + -25 = 14x + 55
5[3((4 + -4x) + x(1 + -1x))] + -1x + -25 = 14x + 55
5[3(4 + -4x + (1 * x + -1x * x))] + -1x + -25 = 14x + 55
5[3(4 + -4x + (1x + -1x2))] + -1x + -25 = 14x + 55

Combine like terms: -4x + 1x = -3x
5[3(4 + -3x + -1x2)] + -1x + -25 = 14x + 55
5[(4 * 3 + -3x * 3 + -1x2 * 3)] + -1x + -25 = 14x + 55
5[(12 + -9x + -3x2)] + -1x + -25 = 14x + 55
[12 * 5 + -9x * 5 + -3x2 * 5] + -1x + -25 = 14x + 55
[60 + -45x + -15x2] + -1x + -25 = 14x + 55

Reorder the terms:
60 + -25 + -45x + -1x + -15x2 = 14x + 55

Combine like terms: 60 + -25 = 35
35 + -45x + -1x + -15x2 = 14x + 55

Combine like terms: -45x + -1x = -46x
35 + -46x + -15x2 = 14x + 55

Reorder the terms:
35 + -46x + -15x2 = 55 + 14x

Solving
35 + -46x + -15x2 = 55 + 14x

Solving for variable 'x'.

Reorder the terms:
35 + -55 + -46x + -14x + -15x2 = 55 + 14x + -55 + -14x

Combine like terms: 35 + -55 = -20
-20 + -46x + -14x + -15x2 = 55 + 14x + -55 + -14x

Combine like terms: -46x + -14x = -60x
-20 + -60x + -15x2 = 55 + 14x + -55 + -14x

Reorder the terms:
-20 + -60x + -15x2 = 55 + -55 + 14x + -14x

Combine like terms: 55 + -55 = 0
-20 + -60x + -15x2 = 0 + 14x + -14x
-20 + -60x + -15x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-20 + -60x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(4 + 12x + 3x2) = 0

Ignore the factor -5.
Subproblem 1
Set the factor '(4 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 12x + 3x2 = 0

Solving
4 + 12x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
1.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 4x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 4x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + -1.333333333
4x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
4x + x2 = -1.333333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1.333333333 + 4

Reorder the terms:
4 + 4x + x2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + 4x + x2 = 2.666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + 2) equal to 1.632993162 and -1.632993162.

Subproblem 1
x + 2 = 1.632993162

Simplifying
x + 2 = 1.632993162

Reorder the terms:
2 + x = 1.632993162

Solving
2 + x = 1.632993162

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.632993162 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.632993162 + -2
x = 1.632993162 + -2

Combine like terms: 1.632993162 + -2 = -0.367006838
x = -0.367006838

Simplifying
x = -0.367006838

Subproblem 2
x + 2 = -1.632993162

Simplifying
x + 2 = -1.632993162

Reorder the terms:
2 + x = -1.632993162

Solving
2 + x = -1.632993162

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.632993162 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.632993162 + -2
x = -1.632993162 + -2

Combine like terms: -1.632993162 + -2 = -3.632993162
x = -3.632993162

Simplifying
x = -3.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.367006838, -3.632993162}
Solution
x = {-0.367006838, -3.632993162}