15-21x=8x+7x(4-3x)

Solution for 15-21x=8x+7x(4-3x) equation:

Simplifying
15 + -21x = 8x + 7x(4 + -3x)
15 + -21x = 8x + (4 * 7x + -3x * 7x)
15 + -21x = 8x + (28x + -21x2)

Combine like terms: 8x + 28x = 36x
15 + -21x = 36x + -21x2

Solving
15 + -21x = 36x + -21x2

Solving for variable 'x'.

Combine like terms: -21x + -36x = -57x
15 + -57x + 21x2 = 36x + -21x2 + -36x + 21x2

Reorder the terms:
15 + -57x + 21x2 = 36x + -36x + -21x2 + 21x2

Combine like terms: 36x + -36x = 0
15 + -57x + 21x2 = 0 + -21x2 + 21x2
15 + -57x + 21x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
15 + -57x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -19x + 7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -19x + 7x2)' equal to zero and attempt to solve:

Simplifying
5 + -19x + 7x2 = 0

Solving
5 + -19x + 7x2 = 0

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

Divide each side by '7'.
0.7142857143 + -2.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -2.714285714x + -0.7142857143 + x2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -2.714285714x + x2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -2.714285714x + x2 = 0 + -0.7142857143
-2.714285714x + x2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-2.714285714x + x2 = -0.7142857143

The x term is -2.714285714x.  Take half its coefficient (-1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
-2.714285714x + 1.841836734 + x2 = -0.7142857143 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714x + x2 = -0.7142857143 + 1.841836734

Combine like terms: -0.7142857143 + 1.841836734 = 1.1275510197
1.841836734 + -2.714285714x + x2 = 1.1275510197

Factor a perfect square on the left side:
(x + -1.357142857)(x + -1.357142857) = 1.1275510197

Calculate the square root of the right side: 1.061862053

Break this problem into two subproblems by setting 
(x + -1.357142857) equal to 1.061862053 and -1.061862053.

Subproblem 1
x + -1.357142857 = 1.061862053

Simplifying
x + -1.357142857 = 1.061862053

Reorder the terms:
-1.357142857 + x = 1.061862053

Solving
-1.357142857 + x = 1.061862053

Solving for variable 'x'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + x = 1.061862053 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = 1.061862053 + 1.357142857
x = 1.061862053 + 1.357142857

Combine like terms: 1.061862053 + 1.357142857 = 2.41900491
x = 2.41900491

Simplifying
x = 2.41900491

Subproblem 2
x + -1.357142857 = -1.061862053

Simplifying
x + -1.357142857 = -1.061862053

Reorder the terms:
-1.357142857 + x = -1.061862053

Solving
-1.357142857 + x = -1.061862053

Solving for variable 'x'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + x = -1.061862053 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + x = -1.061862053 + 1.357142857
x = -1.061862053 + 1.357142857

Combine like terms: -1.061862053 + 1.357142857 = 0.295280804
x = 0.295280804

Simplifying
x = 0.295280804

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.41900491, 0.295280804}
Solution
x = {2.41900491, 0.295280804}