15+(2x-3)=10x(3x-2)

Solution for 15+(2x-3)=10x(3x-2) equation:

Simplifying
15 + (2x + -3) = 10x(3x + -2)

Reorder the terms:
15 + (-3 + 2x) = 10x(3x + -2)

Remove parenthesis around (-3 + 2x)
15 + -3 + 2x = 10x(3x + -2)

Combine like terms: 15 + -3 = 12
12 + 2x = 10x(3x + -2)

Reorder the terms:
12 + 2x = 10x(-2 + 3x)
12 + 2x = (-2 * 10x + 3x * 10x)
12 + 2x = (-20x + 30x2)

Solving
12 + 2x = -20x + 30x2

Solving for variable 'x'.

Combine like terms: 2x + 20x = 22x
12 + 22x + -30x2 = -20x + 30x2 + 20x + -30x2

Reorder the terms:
12 + 22x + -30x2 = -20x + 20x + 30x2 + -30x2

Combine like terms: -20x + 20x = 0
12 + 22x + -30x2 = 0 + 30x2 + -30x2
12 + 22x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
12 + 22x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 11x + -15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 11x + -15x2)' equal to zero and attempt to solve:

Simplifying
6 + 11x + -15x2 = 0

Solving
6 + 11x + -15x2 = 0

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

Divide each side by '-15'.
-0.4 + -0.7333333333x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.7333333333x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.7333333333x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.7333333333x + x2 = 0 + 0.4
-0.7333333333x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.7333333333x + x2 = 0.4

The x term is -0.7333333333x.  Take half its coefficient (-0.3666666667).
Square it (0.1344444445) and add it to both sides.

Add '0.1344444445' to each side of the equation.
-0.7333333333x + 0.1344444445 + x2 = 0.4 + 0.1344444445

Reorder the terms:
0.1344444445 + -0.7333333333x + x2 = 0.4 + 0.1344444445

Combine like terms: 0.4 + 0.1344444445 = 0.5344444445
0.1344444445 + -0.7333333333x + x2 = 0.5344444445

Factor a perfect square on the left side:
(x + -0.3666666667)(x + -0.3666666667) = 0.5344444445

Calculate the square root of the right side: 0.731057073

Break this problem into two subproblems by setting 
(x + -0.3666666667) equal to 0.731057073 and -0.731057073.

Subproblem 1
x + -0.3666666667 = 0.731057073

Simplifying
x + -0.3666666667 = 0.731057073

Reorder the terms:
-0.3666666667 + x = 0.731057073

Solving
-0.3666666667 + x = 0.731057073

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = 0.731057073 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = 0.731057073 + 0.3666666667
x = 0.731057073 + 0.3666666667

Combine like terms: 0.731057073 + 0.3666666667 = 1.0977237397
x = 1.0977237397

Simplifying
x = 1.0977237397

Subproblem 2
x + -0.3666666667 = -0.731057073

Simplifying
x + -0.3666666667 = -0.731057073

Reorder the terms:
-0.3666666667 + x = -0.731057073

Solving
-0.3666666667 + x = -0.731057073

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = -0.731057073 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = -0.731057073 + 0.3666666667
x = -0.731057073 + 0.3666666667

Combine like terms: -0.731057073 + 0.3666666667 = -0.3643904063
x = -0.3643904063

Simplifying
x = -0.3643904063

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0977237397, -0.3643904063}
Solution
x = {1.0977237397, -0.3643904063}