3x-5(x+6)=-2x(x-3)

Solution for 3x-5(x+6)=-2x(x-3) equation:

Simplifying
3x + -5(x + 6) = -2x(x + -3)

Reorder the terms:
3x + -5(6 + x) = -2x(x + -3)
3x + (6 * -5 + x * -5) = -2x(x + -3)
3x + (-30 + -5x) = -2x(x + -3)

Reorder the terms:
-30 + 3x + -5x = -2x(x + -3)

Combine like terms: 3x + -5x = -2x
-30 + -2x = -2x(x + -3)

Reorder the terms:
-30 + -2x = -2x(-3 + x)
-30 + -2x = (-3 * -2x + x * -2x)
-30 + -2x = (6x + -2x2)

Solving
-30 + -2x = 6x + -2x2

Solving for variable 'x'.

Combine like terms: -2x + -6x = -8x
-30 + -8x + 2x2 = 6x + -2x2 + -6x + 2x2

Reorder the terms:
-30 + -8x + 2x2 = 6x + -6x + -2x2 + 2x2

Combine like terms: 6x + -6x = 0
-30 + -8x + 2x2 = 0 + -2x2 + 2x2
-30 + -8x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-30 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -4x + x2 = 0

Solving
-15 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -4x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -4x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4x + x2 = 0 + 15
-4x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-4x + x2 = 15

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 = 15 + 4

Reorder the terms:
4 + -4x + x2 = 15 + 4

Combine like terms: 15 + 4 = 19
4 + -4x + x2 = 19

Factor a perfect square on the left side:
(x + -2)(x + -2) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -2) equal to 4.358898944 and -4.358898944.

Subproblem 1
x + -2 = 4.358898944

Simplifying
x + -2 = 4.358898944

Reorder the terms:
-2 + x = 4.358898944

Solving
-2 + x = 4.358898944

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 = 4.358898944 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.358898944 + 2
x = 4.358898944 + 2

Combine like terms: 4.358898944 + 2 = 6.358898944
x = 6.358898944

Simplifying
x = 6.358898944

Subproblem 2
x + -2 = -4.358898944

Simplifying
x + -2 = -4.358898944

Reorder the terms:
-2 + x = -4.358898944

Solving
-2 + x = -4.358898944

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 = -4.358898944 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.358898944 + 2
x = -4.358898944 + 2

Combine like terms: -4.358898944 + 2 = -2.358898944
x = -2.358898944

Simplifying
x = -2.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.358898944, -2.358898944}
Solution
x = {6.358898944, -2.358898944}