81=15x(x-7)

Solution for 81=15x(x-7) equation:

Simplifying
81 = 15x(x + -7)

Reorder the terms:
81 = 15x(-7 + x)
81 = (-7 * 15x + x * 15x)
81 = (-105x + 15x2)

Solving
81 = -105x + 15x2

Solving for variable 'x'.

Reorder the terms:
81 + 105x + -15x2 = -105x + 105x + 15x2 + -15x2

Combine like terms: -105x + 105x = 0
81 + 105x + -15x2 = 0 + 15x2 + -15x2
81 + 105x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
81 + 105x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + 35x + -5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(27 + 35x + -5x2)' equal to zero and attempt to solve:

Simplifying
27 + 35x + -5x2 = 0

Solving
27 + 35x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-5.4 + -7x + x2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + -7x + 5.4 + x2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + -7x + x2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + -7x + x2 = 0 + 5.4
-7x + x2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
-7x + x2 = 5.4

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 5.4 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 5.4 + 12.25

Combine like terms: 5.4 + 12.25 = 17.65
12.25 + -7x + x2 = 17.65

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 17.65

Calculate the square root of the right side: 4.201190308

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.201190308 and -4.201190308.

Subproblem 1
x + -3.5 = 4.201190308

Simplifying
x + -3.5 = 4.201190308

Reorder the terms:
-3.5 + x = 4.201190308

Solving
-3.5 + x = 4.201190308

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.201190308 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.201190308 + 3.5
x = 4.201190308 + 3.5

Combine like terms: 4.201190308 + 3.5 = 7.701190308
x = 7.701190308

Simplifying
x = 7.701190308

Subproblem 2
x + -3.5 = -4.201190308

Simplifying
x + -3.5 = -4.201190308

Reorder the terms:
-3.5 + x = -4.201190308

Solving
-3.5 + x = -4.201190308

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.201190308 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.201190308 + 3.5
x = -4.201190308 + 3.5

Combine like terms: -4.201190308 + 3.5 = -0.701190308
x = -0.701190308

Simplifying
x = -0.701190308

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.701190308, -0.701190308}
Solution
x = {7.701190308, -0.701190308}