(3x(15+2x(5+5)))-25=

Solution for (3x(15+2x(5+5)))-25= equation:

Simplifying
(3x(15 + 2x(5 + 5))) + -25 = 0

Combine like terms: 5 + 5 = 10
(3x(15 + 2x(10))) + -25 = 0

Reorder the terms for easier multiplication:
(3x(15 + 2 * 10x)) + -25 = 0

Multiply 2 * 10
(3x(15 + 20x)) + -25 = 0
((15 * 3x + 20x * 3x)) + -25 = 0
((45x + 60x2)) + -25 = 0
(45x + 60x2) + -25 = 0

Remove parenthesis around (45x + 60x2)
45x + 60x2 + -25 = 0

Reorder the terms:
-25 + 45x + 60x2 = 0

Solving
-25 + 45x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 9x + 12x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-5 + 9x + 12x2)' equal to zero and attempt to solve:

Simplifying
-5 + 9x + 12x2 = 0

Solving
-5 + 9x + 12x2 = 0

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

Divide each side by '12'.
-0.4166666667 + 0.75x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.75x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 0.75x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 0.75x + x2 = 0 + 0.4166666667
0.75x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
0.75x + x2 = 0.4166666667

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 0.4166666667 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 0.4166666667 + 0.140625

Combine like terms: 0.4166666667 + 0.140625 = 0.5572916667
0.140625 + 0.75x + x2 = 0.5572916667

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.5572916667

Calculate the square root of the right side: 0.746519703

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.746519703 and -0.746519703.

Subproblem 1
x + 0.375 = 0.746519703

Simplifying
x + 0.375 = 0.746519703

Reorder the terms:
0.375 + x = 0.746519703

Solving
0.375 + x = 0.746519703

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.746519703 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.746519703 + -0.375
x = 0.746519703 + -0.375

Combine like terms: 0.746519703 + -0.375 = 0.371519703
x = 0.371519703

Simplifying
x = 0.371519703

Subproblem 2
x + 0.375 = -0.746519703

Simplifying
x + 0.375 = -0.746519703

Reorder the terms:
0.375 + x = -0.746519703

Solving
0.375 + x = -0.746519703

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.746519703 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.746519703 + -0.375
x = -0.746519703 + -0.375

Combine like terms: -0.746519703 + -0.375 = -1.121519703
x = -1.121519703

Simplifying
x = -1.121519703

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.371519703, -1.121519703}
Solution
x = {0.371519703, -1.121519703}