x=1.05(x-15)(x+12)

Solution for x=1.05(x-15)(x+12) equation:

Simplifying
x = 1.05(x + -15)(x + 12)

Reorder the terms:
x = 1.05(-15 + x)(x + 12)

Reorder the terms:
x = 1.05(-15 + x)(12 + x)

Multiply (-15 + x) * (12 + x)
x = 1.05(-15(12 + x) + x(12 + x))
x = 1.05((12 * -15 + x * -15) + x(12 + x))
x = 1.05((-180 + -15x) + x(12 + x))
x = 1.05(-180 + -15x + (12 * x + x * x))
x = 1.05(-180 + -15x + (12x + x2))

Combine like terms: -15x + 12x = -3x
x = 1.05(-180 + -3x + x2)
x = (-180 * 1.05 + -3x * 1.05 + x2 * 1.05)
x = (-189 + -3.15x + 1.05x2)

Solving
x = -189 + -3.15x + 1.05x2

Solving for variable 'x'.

Reorder the terms:
189 + x + 3.15x + -1.05x2 = -189 + -3.15x + 1.05x2 + 189 + 3.15x + -1.05x2

Combine like terms: x + 3.15x = 4.15x
189 + 4.15x + -1.05x2 = -189 + -3.15x + 1.05x2 + 189 + 3.15x + -1.05x2

Reorder the terms:
189 + 4.15x + -1.05x2 = -189 + 189 + -3.15x + 3.15x + 1.05x2 + -1.05x2

Combine like terms: -189 + 189 = 0
189 + 4.15x + -1.05x2 = 0 + -3.15x + 3.15x + 1.05x2 + -1.05x2
189 + 4.15x + -1.05x2 = -3.15x + 3.15x + 1.05x2 + -1.05x2

Combine like terms: -3.15x + 3.15x = 0.00
189 + 4.15x + -1.05x2 = 0.00 + 1.05x2 + -1.05x2
189 + 4.15x + -1.05x2 = 1.05x2 + -1.05x2

Combine like terms: 1.05x2 + -1.05x2 = 0.00
189 + 4.15x + -1.05x2 = 0.00

Begin completing the square.  Divide all terms by
-1.05 the coefficient of the squared term: 

Divide each side by '-1.05'.
-180 + -3.952380952x + x2 = 0

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -3.952380952x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -3.952380952x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -3.952380952x + x2 = 0 + 180
-3.952380952x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-3.952380952x + x2 = 180

The x term is -3.952380952x.  Take half its coefficient (-1.976190476).
Square it (3.905328797) and add it to both sides.

Add '3.905328797' to each side of the equation.
-3.952380952x + 3.905328797 + x2 = 180 + 3.905328797

Reorder the terms:
3.905328797 + -3.952380952x + x2 = 180 + 3.905328797

Combine like terms: 180 + 3.905328797 = 183.905328797
3.905328797 + -3.952380952x + x2 = 183.905328797

Factor a perfect square on the left side:
(x + -1.976190476)(x + -1.976190476) = 183.905328797

Calculate the square root of the right side: 13.56116989

Break this problem into two subproblems by setting 
(x + -1.976190476) equal to 13.56116989 and -13.56116989.

Subproblem 1
x + -1.976190476 = 13.56116989

Simplifying
x + -1.976190476 = 13.56116989

Reorder the terms:
-1.976190476 + x = 13.56116989

Solving
-1.976190476 + x = 13.56116989

Solving for variable 'x'.

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

Add '1.976190476' to each side of the equation.
-1.976190476 + 1.976190476 + x = 13.56116989 + 1.976190476

Combine like terms: -1.976190476 + 1.976190476 = 0.000000000
0.000000000 + x = 13.56116989 + 1.976190476
x = 13.56116989 + 1.976190476

Combine like terms: 13.56116989 + 1.976190476 = 15.537360366
x = 15.537360366

Simplifying
x = 15.537360366

Subproblem 2
x + -1.976190476 = -13.56116989

Simplifying
x + -1.976190476 = -13.56116989

Reorder the terms:
-1.976190476 + x = -13.56116989

Solving
-1.976190476 + x = -13.56116989

Solving for variable 'x'.

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

Add '1.976190476' to each side of the equation.
-1.976190476 + 1.976190476 + x = -13.56116989 + 1.976190476

Combine like terms: -1.976190476 + 1.976190476 = 0.000000000
0.000000000 + x = -13.56116989 + 1.976190476
x = -13.56116989 + 1.976190476

Combine like terms: -13.56116989 + 1.976190476 = -11.584979414
x = -11.584979414

Simplifying
x = -11.584979414

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.537360366, -11.584979414}