-3x(x+5)=3(x-1)

Solution for -3x(x+5)=3(x-1) equation:

Simplifying
-3x(x + 5) = 3(x + -1)

Reorder the terms:
-3x(5 + x) = 3(x + -1)
(5 * -3x + x * -3x) = 3(x + -1)
(-15x + -3x2) = 3(x + -1)

Reorder the terms:
-15x + -3x2 = 3(-1 + x)
-15x + -3x2 = (-1 * 3 + x * 3)
-15x + -3x2 = (-3 + 3x)

Solving
-15x + -3x2 = -3 + 3x

Solving for variable 'x'.

Reorder the terms:
3 + -15x + -3x + -3x2 = -3 + 3x + 3 + -3x

Combine like terms: -15x + -3x = -18x
3 + -18x + -3x2 = -3 + 3x + 3 + -3x

Reorder the terms:
3 + -18x + -3x2 = -3 + 3 + 3x + -3x

Combine like terms: -3 + 3 = 0
3 + -18x + -3x2 = 0 + 3x + -3x
3 + -18x + -3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
3 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -6x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x + -1x2 = 0

Solving
1 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x + x2 = 0 + 1
6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6x + x2 = 1

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 3 = 3.16227766

Simplifying
x + 3 = 3.16227766

Reorder the terms:
3 + x = 3.16227766

Solving
3 + x = 3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.16227766 + -3
x = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
x = 0.16227766

Simplifying
x = 0.16227766

Subproblem 2
x + 3 = -3.16227766

Simplifying
x + 3 = -3.16227766

Reorder the terms:
3 + x = -3.16227766

Solving
3 + x = -3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.16227766 + -3
x = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
x = -6.16227766

Simplifying
x = -6.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.16227766, -6.16227766}
Solution
x = {0.16227766, -6.16227766}