15(14x-20)=14x(x+3)

Solution for 15(14x-20)=14x(x+3) equation:

Simplifying
15(14x + -20) = 14x(x + 3)

Reorder the terms:
15(-20 + 14x) = 14x(x + 3)
(-20 * 15 + 14x * 15) = 14x(x + 3)
(-300 + 210x) = 14x(x + 3)

Reorder the terms:
-300 + 210x = 14x(3 + x)
-300 + 210x = (3 * 14x + x * 14x)
-300 + 210x = (42x + 14x2)

Solving
-300 + 210x = 42x + 14x2

Solving for variable 'x'.

Combine like terms: 210x + -42x = 168x
-300 + 168x + -14x2 = 42x + 14x2 + -42x + -14x2

Reorder the terms:
-300 + 168x + -14x2 = 42x + -42x + 14x2 + -14x2

Combine like terms: 42x + -42x = 0
-300 + 168x + -14x2 = 0 + 14x2 + -14x2
-300 + 168x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-300 + 168x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-150 + 84x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-150 + 84x + -7x2)' equal to zero and attempt to solve:

Simplifying
-150 + 84x + -7x2 = 0

Solving
-150 + 84x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
21.42857143 + -12x + x2 = 0

Move the constant term to the right:

Add '-21.42857143' to each side of the equation.
21.42857143 + -12x + -21.42857143 + x2 = 0 + -21.42857143

Reorder the terms:
21.42857143 + -21.42857143 + -12x + x2 = 0 + -21.42857143

Combine like terms: 21.42857143 + -21.42857143 = 0.00000000
0.00000000 + -12x + x2 = 0 + -21.42857143
-12x + x2 = 0 + -21.42857143

Combine like terms: 0 + -21.42857143 = -21.42857143
-12x + x2 = -21.42857143

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -21.42857143 + 36

Reorder the terms:
36 + -12x + x2 = -21.42857143 + 36

Combine like terms: -21.42857143 + 36 = 14.57142857
36 + -12x + x2 = 14.57142857

Factor a perfect square on the left side:
(x + -6)(x + -6) = 14.57142857

Calculate the square root of the right side: 3.817254061

Break this problem into two subproblems by setting 
(x + -6) equal to 3.817254061 and -3.817254061.

Subproblem 1
x + -6 = 3.817254061

Simplifying
x + -6 = 3.817254061

Reorder the terms:
-6 + x = 3.817254061

Solving
-6 + x = 3.817254061

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 3.817254061 + 6

Combine like terms: -6 + 6 = 0
0 + x = 3.817254061 + 6
x = 3.817254061 + 6

Combine like terms: 3.817254061 + 6 = 9.817254061
x = 9.817254061

Simplifying
x = 9.817254061

Subproblem 2
x + -6 = -3.817254061

Simplifying
x + -6 = -3.817254061

Reorder the terms:
-6 + x = -3.817254061

Solving
-6 + x = -3.817254061

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -3.817254061 + 6

Combine like terms: -6 + 6 = 0
0 + x = -3.817254061 + 6
x = -3.817254061 + 6

Combine like terms: -3.817254061 + 6 = 2.182745939
x = 2.182745939

Simplifying
x = 2.182745939

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.817254061, 2.182745939}
Solution
x = {9.817254061, 2.182745939}