(3+5x)(2-3x)=12-15x*2

Solution for (3+5x)(2-3x)=12-15x*2 equation:

Simplifying
(3 + 5x)(2 + -3x) = 12 + -15x * 2

Multiply (3 + 5x) * (2 + -3x)
(3(2 + -3x) + 5x * (2 + -3x)) = 12 + -15x * 2
((2 * 3 + -3x * 3) + 5x * (2 + -3x)) = 12 + -15x * 2
((6 + -9x) + 5x * (2 + -3x)) = 12 + -15x * 2
(6 + -9x + (2 * 5x + -3x * 5x)) = 12 + -15x * 2
(6 + -9x + (10x + -15x2)) = 12 + -15x * 2

Combine like terms: -9x + 10x = 1x
(6 + 1x + -15x2) = 12 + -15x * 2

Reorder the terms for easier multiplication:
6 + 1x + -15x2 = 12 + -15 * 2x

Multiply -15 * 2
6 + 1x + -15x2 = 12 + -30x

Solving
6 + 1x + -15x2 = 12 + -30x

Solving for variable 'x'.

Reorder the terms:
6 + -12 + 1x + 30x + -15x2 = 12 + -30x + -12 + 30x

Combine like terms: 6 + -12 = -6
-6 + 1x + 30x + -15x2 = 12 + -30x + -12 + 30x

Combine like terms: 1x + 30x = 31x
-6 + 31x + -15x2 = 12 + -30x + -12 + 30x

Reorder the terms:
-6 + 31x + -15x2 = 12 + -12 + -30x + 30x

Combine like terms: 12 + -12 = 0
-6 + 31x + -15x2 = 0 + -30x + 30x
-6 + 31x + -15x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-6 + 31x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.4 + -2.066666667x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.066666667x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.066666667x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.066666667x + x2 = 0 + -0.4
-2.066666667x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.066666667x + x2 = -0.4

The x term is -2.066666667x.  Take half its coefficient (-1.033333334).
Square it (1.067777779) and add it to both sides.

Add '1.067777779' to each side of the equation.
-2.066666667x + 1.067777779 + x2 = -0.4 + 1.067777779

Reorder the terms:
1.067777779 + -2.066666667x + x2 = -0.4 + 1.067777779

Combine like terms: -0.4 + 1.067777779 = 0.667777779
1.067777779 + -2.066666667x + x2 = 0.667777779

Factor a perfect square on the left side:
(x + -1.033333334)(x + -1.033333334) = 0.667777779

Calculate the square root of the right side: 0.817176712

Break this problem into two subproblems by setting 
(x + -1.033333334) equal to 0.817176712 and -0.817176712.

Subproblem 1
x + -1.033333334 = 0.817176712

Simplifying
x + -1.033333334 = 0.817176712

Reorder the terms:
-1.033333334 + x = 0.817176712

Solving
-1.033333334 + x = 0.817176712

Solving for variable 'x'.

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

Add '1.033333334' to each side of the equation.
-1.033333334 + 1.033333334 + x = 0.817176712 + 1.033333334

Combine like terms: -1.033333334 + 1.033333334 = 0.000000000
0.000000000 + x = 0.817176712 + 1.033333334
x = 0.817176712 + 1.033333334

Combine like terms: 0.817176712 + 1.033333334 = 1.850510046
x = 1.850510046

Simplifying
x = 1.850510046

Subproblem 2
x + -1.033333334 = -0.817176712

Simplifying
x + -1.033333334 = -0.817176712

Reorder the terms:
-1.033333334 + x = -0.817176712

Solving
-1.033333334 + x = -0.817176712

Solving for variable 'x'.

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

Add '1.033333334' to each side of the equation.
-1.033333334 + 1.033333334 + x = -0.817176712 + 1.033333334

Combine like terms: -1.033333334 + 1.033333334 = 0.000000000
0.000000000 + x = -0.817176712 + 1.033333334
x = -0.817176712 + 1.033333334

Combine like terms: -0.817176712 + 1.033333334 = 0.216156622
x = 0.216156622

Simplifying
x = 0.216156622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.850510046, 0.216156622}