1(3x-3)+1(3x+4)=(15x+20)(3x-3)

Solution for 1(3x-3)+1(3x+4)=(15x+20)(3x-3) equation:

Simplifying
1(3x + -3) + 1(3x + 4) = (15x + 20)(3x + -3)

Reorder the terms:
1(-3 + 3x) + 1(3x + 4) = (15x + 20)(3x + -3)
(-3 * 1 + 3x * 1) + 1(3x + 4) = (15x + 20)(3x + -3)
(-3 + 3x) + 1(3x + 4) = (15x + 20)(3x + -3)

Reorder the terms:
-3 + 3x + 1(4 + 3x) = (15x + 20)(3x + -3)
-3 + 3x + (4 * 1 + 3x * 1) = (15x + 20)(3x + -3)
-3 + 3x + (4 + 3x) = (15x + 20)(3x + -3)

Reorder the terms:
-3 + 4 + 3x + 3x = (15x + 20)(3x + -3)

Combine like terms: -3 + 4 = 1
1 + 3x + 3x = (15x + 20)(3x + -3)

Combine like terms: 3x + 3x = 6x
1 + 6x = (15x + 20)(3x + -3)

Reorder the terms:
1 + 6x = (20 + 15x)(3x + -3)

Reorder the terms:
1 + 6x = (20 + 15x)(-3 + 3x)

Multiply (20 + 15x) * (-3 + 3x)
1 + 6x = (20(-3 + 3x) + 15x * (-3 + 3x))
1 + 6x = ((-3 * 20 + 3x * 20) + 15x * (-3 + 3x))
1 + 6x = ((-60 + 60x) + 15x * (-3 + 3x))
1 + 6x = (-60 + 60x + (-3 * 15x + 3x * 15x))
1 + 6x = (-60 + 60x + (-45x + 45x2))

Combine like terms: 60x + -45x = 15x
1 + 6x = (-60 + 15x + 45x2)

Solving
1 + 6x = -60 + 15x + 45x2

Solving for variable 'x'.

Reorder the terms:
1 + 60 + 6x + -15x + -45x2 = -60 + 15x + 45x2 + 60 + -15x + -45x2

Combine like terms: 1 + 60 = 61
61 + 6x + -15x + -45x2 = -60 + 15x + 45x2 + 60 + -15x + -45x2

Combine like terms: 6x + -15x = -9x
61 + -9x + -45x2 = -60 + 15x + 45x2 + 60 + -15x + -45x2

Reorder the terms:
61 + -9x + -45x2 = -60 + 60 + 15x + -15x + 45x2 + -45x2

Combine like terms: -60 + 60 = 0
61 + -9x + -45x2 = 0 + 15x + -15x + 45x2 + -45x2
61 + -9x + -45x2 = 15x + -15x + 45x2 + -45x2

Combine like terms: 15x + -15x = 0
61 + -9x + -45x2 = 0 + 45x2 + -45x2
61 + -9x + -45x2 = 45x2 + -45x2

Combine like terms: 45x2 + -45x2 = 0
61 + -9x + -45x2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
-1.355555556 + 0.2x + x2 = 0

Move the constant term to the right:

Add '1.355555556' to each side of the equation.
-1.355555556 + 0.2x + 1.355555556 + x2 = 0 + 1.355555556

Reorder the terms:
-1.355555556 + 1.355555556 + 0.2x + x2 = 0 + 1.355555556

Combine like terms: -1.355555556 + 1.355555556 = 0.000000000
0.000000000 + 0.2x + x2 = 0 + 1.355555556
0.2x + x2 = 0 + 1.355555556

Combine like terms: 0 + 1.355555556 = 1.355555556
0.2x + x2 = 1.355555556

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 1.355555556 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 1.355555556 + 0.01

Combine like terms: 1.355555556 + 0.01 = 1.365555556
0.01 + 0.2x + x2 = 1.365555556

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 1.365555556

Calculate the square root of the right side: 1.168569876

Break this problem into two subproblems by setting 
(x + 0.1) equal to 1.168569876 and -1.168569876.

Subproblem 1
x + 0.1 = 1.168569876

Simplifying
x + 0.1 = 1.168569876

Reorder the terms:
0.1 + x = 1.168569876

Solving
0.1 + x = 1.168569876

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = 1.168569876 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 1.168569876 + -0.1
x = 1.168569876 + -0.1

Combine like terms: 1.168569876 + -0.1 = 1.068569876
x = 1.068569876

Simplifying
x = 1.068569876

Subproblem 2
x + 0.1 = -1.168569876

Simplifying
x + 0.1 = -1.168569876

Reorder the terms:
0.1 + x = -1.168569876

Solving
0.1 + x = -1.168569876

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = -1.168569876 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -1.168569876 + -0.1
x = -1.168569876 + -0.1

Combine like terms: -1.168569876 + -0.1 = -1.268569876
x = -1.268569876

Simplifying
x = -1.268569876

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.068569876, -1.268569876}