5[3(x+4)-2(1-x)]x-15=14x+45

Solution for 5[3(x+4)-2(1-x)]x-15=14x+45 equation:

Simplifying
5[3(x + 4) + -2(1 + -1x)] * x + -15 = 14x + 45

Reorder the terms:
5[3(4 + x) + -2(1 + -1x)] * x + -15 = 14x + 45
5[(4 * 3 + x * 3) + -2(1 + -1x)] * x + -15 = 14x + 45
5[(12 + 3x) + -2(1 + -1x)] * x + -15 = 14x + 45
5[12 + 3x + (1 * -2 + -1x * -2)] * x + -15 = 14x + 45
5[12 + 3x + (-2 + 2x)] * x + -15 = 14x + 45

Reorder the terms:
5[12 + -2 + 3x + 2x] * x + -15 = 14x + 45

Combine like terms: 12 + -2 = 10
5[10 + 3x + 2x] * x + -15 = 14x + 45

Combine like terms: 3x + 2x = 5x
5[10 + 5x] * x + -15 = 14x + 45

Reorder the terms for easier multiplication:
5x[10 + 5x] + -15 = 14x + 45
[10 * 5x + 5x * 5x] + -15 = 14x + 45
[50x + 25x2] + -15 = 14x + 45

Reorder the terms:
-15 + 50x + 25x2 = 14x + 45

Reorder the terms:
-15 + 50x + 25x2 = 45 + 14x

Solving
-15 + 50x + 25x2 = 45 + 14x

Solving for variable 'x'.

Reorder the terms:
-15 + -45 + 50x + -14x + 25x2 = 45 + 14x + -45 + -14x

Combine like terms: -15 + -45 = -60
-60 + 50x + -14x + 25x2 = 45 + 14x + -45 + -14x

Combine like terms: 50x + -14x = 36x
-60 + 36x + 25x2 = 45 + 14x + -45 + -14x

Reorder the terms:
-60 + 36x + 25x2 = 45 + -45 + 14x + -14x

Combine like terms: 45 + -45 = 0
-60 + 36x + 25x2 = 0 + 14x + -14x
-60 + 36x + 25x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-60 + 36x + 25x2 = 0

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

Divide each side by '25'.
-2.4 + 1.44x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 1.44x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 1.44x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 1.44x + x2 = 0 + 2.4
1.44x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
1.44x + x2 = 2.4

The x term is 1.44x.  Take half its coefficient (0.72).
Square it (0.5184) and add it to both sides.

Add '0.5184' to each side of the equation.
1.44x + 0.5184 + x2 = 2.4 + 0.5184

Reorder the terms:
0.5184 + 1.44x + x2 = 2.4 + 0.5184

Combine like terms: 2.4 + 0.5184 = 2.9184
0.5184 + 1.44x + x2 = 2.9184

Factor a perfect square on the left side:
(x + 0.72)(x + 0.72) = 2.9184

Calculate the square root of the right side: 1.70833252

Break this problem into two subproblems by setting 
(x + 0.72) equal to 1.70833252 and -1.70833252.

Subproblem 1
x + 0.72 = 1.70833252

Simplifying
x + 0.72 = 1.70833252

Reorder the terms:
0.72 + x = 1.70833252

Solving
0.72 + x = 1.70833252

Solving for variable 'x'.

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

Add '-0.72' to each side of the equation.
0.72 + -0.72 + x = 1.70833252 + -0.72

Combine like terms: 0.72 + -0.72 = 0.00
0.00 + x = 1.70833252 + -0.72
x = 1.70833252 + -0.72

Combine like terms: 1.70833252 + -0.72 = 0.98833252
x = 0.98833252

Simplifying
x = 0.98833252

Subproblem 2
x + 0.72 = -1.70833252

Simplifying
x + 0.72 = -1.70833252

Reorder the terms:
0.72 + x = -1.70833252

Solving
0.72 + x = -1.70833252

Solving for variable 'x'.

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

Add '-0.72' to each side of the equation.
0.72 + -0.72 + x = -1.70833252 + -0.72

Combine like terms: 0.72 + -0.72 = 0.00
0.00 + x = -1.70833252 + -0.72
x = -1.70833252 + -0.72

Combine like terms: -1.70833252 + -0.72 = -2.42833252
x = -2.42833252

Simplifying
x = -2.42833252

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.98833252, -2.42833252}