3x-3(x^2+5)=5x(x+5)-9

Solution for 3x-3(x^2+5)=5x(x+5)-9 equation:

Simplifying
3x + -3(x2 + 5) = 5x(x + 5) + -9

Reorder the terms:
3x + -3(5 + x2) = 5x(x + 5) + -9
3x + (5 * -3 + x2 * -3) = 5x(x + 5) + -9
3x + (-15 + -3x2) = 5x(x + 5) + -9

Reorder the terms:
-15 + 3x + -3x2 = 5x(x + 5) + -9

Reorder the terms:
-15 + 3x + -3x2 = 5x(5 + x) + -9
-15 + 3x + -3x2 = (5 * 5x + x * 5x) + -9
-15 + 3x + -3x2 = (25x + 5x2) + -9

Reorder the terms:
-15 + 3x + -3x2 = -9 + 25x + 5x2

Solving
-15 + 3x + -3x2 = -9 + 25x + 5x2

Solving for variable 'x'.

Reorder the terms:
-15 + 9 + 3x + -25x + -3x2 + -5x2 = -9 + 25x + 5x2 + 9 + -25x + -5x2

Combine like terms: -15 + 9 = -6
-6 + 3x + -25x + -3x2 + -5x2 = -9 + 25x + 5x2 + 9 + -25x + -5x2

Combine like terms: 3x + -25x = -22x
-6 + -22x + -3x2 + -5x2 = -9 + 25x + 5x2 + 9 + -25x + -5x2

Combine like terms: -3x2 + -5x2 = -8x2
-6 + -22x + -8x2 = -9 + 25x + 5x2 + 9 + -25x + -5x2

Reorder the terms:
-6 + -22x + -8x2 = -9 + 9 + 25x + -25x + 5x2 + -5x2

Combine like terms: -9 + 9 = 0
-6 + -22x + -8x2 = 0 + 25x + -25x + 5x2 + -5x2
-6 + -22x + -8x2 = 25x + -25x + 5x2 + -5x2

Combine like terms: 25x + -25x = 0
-6 + -22x + -8x2 = 0 + 5x2 + -5x2
-6 + -22x + -8x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + -22x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 11x + 4x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 11x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 11x + 4x2 = 0

Solving
3 + 11x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 2.75x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.75x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.75x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.75x + x2 = 0 + -0.75
2.75x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.75x + x2 = -0.75

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = -0.75 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = -0.75 + 1.890625

Combine like terms: -0.75 + 1.890625 = 1.140625
1.890625 + 2.75x + x2 = 1.140625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + 1.375) equal to 1.068000468 and -1.068000468.

Subproblem 1
x + 1.375 = 1.068000468

Simplifying
x + 1.375 = 1.068000468

Reorder the terms:
1.375 + x = 1.068000468

Solving
1.375 + x = 1.068000468

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = 1.068000468 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 1.068000468 + -1.375
x = 1.068000468 + -1.375

Combine like terms: 1.068000468 + -1.375 = -0.306999532
x = -0.306999532

Simplifying
x = -0.306999532

Subproblem 2
x + 1.375 = -1.068000468

Simplifying
x + 1.375 = -1.068000468

Reorder the terms:
1.375 + x = -1.068000468

Solving
1.375 + x = -1.068000468

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = -1.068000468 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -1.068000468 + -1.375
x = -1.068000468 + -1.375

Combine like terms: -1.068000468 + -1.375 = -2.443000468
x = -2.443000468

Simplifying
x = -2.443000468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.306999532, -2.443000468}
Solution
x = {-0.306999532, -2.443000468}