2[x(4x+15)+5]=2(x+10)

Solution for 2[x(4x+15)+5]=2(x+10) equation:

Simplifying
2[x(4x + 15) + 5] = 2(x + 10)

Reorder the terms:
2[x(15 + 4x) + 5] = 2(x + 10)
2[(15 * x + 4x * x) + 5] = 2(x + 10)
2[(15x + 4x2) + 5] = 2(x + 10)

Reorder the terms:
2[5 + 15x + 4x2] = 2(x + 10)
[5 * 2 + 15x * 2 + 4x2 * 2] = 2(x + 10)
[10 + 30x + 8x2] = 2(x + 10)

Reorder the terms:
10 + 30x + 8x2 = 2(10 + x)
10 + 30x + 8x2 = (10 * 2 + x * 2)
10 + 30x + 8x2 = (20 + 2x)

Solving
10 + 30x + 8x2 = 20 + 2x

Solving for variable 'x'.

Reorder the terms:
10 + -20 + 30x + -2x + 8x2 = 20 + 2x + -20 + -2x

Combine like terms: 10 + -20 = -10
-10 + 30x + -2x + 8x2 = 20 + 2x + -20 + -2x

Combine like terms: 30x + -2x = 28x
-10 + 28x + 8x2 = 20 + 2x + -20 + -2x

Reorder the terms:
-10 + 28x + 8x2 = 20 + -20 + 2x + -2x

Combine like terms: 20 + -20 = 0
-10 + 28x + 8x2 = 0 + 2x + -2x
-10 + 28x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + 28x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 14x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 14x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + 14x + 4x2 = 0

Solving
-5 + 14x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + 3.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 3.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 3.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 3.5x + x2 = 0 + 1.25
3.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
3.5x + x2 = 1.25

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 1.25 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 1.25 + 3.0625

Combine like terms: 1.25 + 3.0625 = 4.3125
3.0625 + 3.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.076655966 and -2.076655966.

Subproblem 1
x + 1.75 = 2.076655966

Simplifying
x + 1.75 = 2.076655966

Reorder the terms:
1.75 + x = 2.076655966

Solving
1.75 + x = 2.076655966

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.076655966 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.076655966 + -1.75
x = 2.076655966 + -1.75

Combine like terms: 2.076655966 + -1.75 = 0.326655966
x = 0.326655966

Simplifying
x = 0.326655966

Subproblem 2
x + 1.75 = -2.076655966

Simplifying
x + 1.75 = -2.076655966

Reorder the terms:
1.75 + x = -2.076655966

Solving
1.75 + x = -2.076655966

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.076655966 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.076655966 + -1.75
x = -2.076655966 + -1.75

Combine like terms: -2.076655966 + -1.75 = -3.826655966
x = -3.826655966

Simplifying
x = -3.826655966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.326655966, -3.826655966}
Solution
x = {0.326655966, -3.826655966}