10(x-9)(5-6x)=2(4x-1)+5(1+2x)

Solution for 10(x-9)(5-6x)=2(4x-1)+5(1+2x) equation:

Simplifying
10(x + -9)(5 + -6x) = 2(4x + -1) + 5(1 + 2x)

Reorder the terms:
10(-9 + x)(5 + -6x) = 2(4x + -1) + 5(1 + 2x)

Multiply (-9 + x) * (5 + -6x)
10(-9(5 + -6x) + x(5 + -6x)) = 2(4x + -1) + 5(1 + 2x)
10((5 * -9 + -6x * -9) + x(5 + -6x)) = 2(4x + -1) + 5(1 + 2x)
10((-45 + 54x) + x(5 + -6x)) = 2(4x + -1) + 5(1 + 2x)
10(-45 + 54x + (5 * x + -6x * x)) = 2(4x + -1) + 5(1 + 2x)
10(-45 + 54x + (5x + -6x2)) = 2(4x + -1) + 5(1 + 2x)

Combine like terms: 54x + 5x = 59x
10(-45 + 59x + -6x2) = 2(4x + -1) + 5(1 + 2x)
(-45 * 10 + 59x * 10 + -6x2 * 10) = 2(4x + -1) + 5(1 + 2x)
(-450 + 590x + -60x2) = 2(4x + -1) + 5(1 + 2x)

Reorder the terms:
-450 + 590x + -60x2 = 2(-1 + 4x) + 5(1 + 2x)
-450 + 590x + -60x2 = (-1 * 2 + 4x * 2) + 5(1 + 2x)
-450 + 590x + -60x2 = (-2 + 8x) + 5(1 + 2x)
-450 + 590x + -60x2 = -2 + 8x + (1 * 5 + 2x * 5)
-450 + 590x + -60x2 = -2 + 8x + (5 + 10x)

Reorder the terms:
-450 + 590x + -60x2 = -2 + 5 + 8x + 10x

Combine like terms: -2 + 5 = 3
-450 + 590x + -60x2 = 3 + 8x + 10x

Combine like terms: 8x + 10x = 18x
-450 + 590x + -60x2 = 3 + 18x

Solving
-450 + 590x + -60x2 = 3 + 18x

Solving for variable 'x'.

Reorder the terms:
-450 + -3 + 590x + -18x + -60x2 = 3 + 18x + -3 + -18x

Combine like terms: -450 + -3 = -453
-453 + 590x + -18x + -60x2 = 3 + 18x + -3 + -18x

Combine like terms: 590x + -18x = 572x
-453 + 572x + -60x2 = 3 + 18x + -3 + -18x

Reorder the terms:
-453 + 572x + -60x2 = 3 + -3 + 18x + -18x

Combine like terms: 3 + -3 = 0
-453 + 572x + -60x2 = 0 + 18x + -18x
-453 + 572x + -60x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-453 + 572x + -60x2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
7.55 + -9.533333333x + x2 = 0.0

Move the constant term to the right:

Add '-7.55' to each side of the equation.
7.55 + -9.533333333x + -7.55 + x2 = 0.0 + -7.55

Reorder the terms:
7.55 + -7.55 + -9.533333333x + x2 = 0.0 + -7.55

Combine like terms: 7.55 + -7.55 = 0.00
0.00 + -9.533333333x + x2 = 0.0 + -7.55
-9.533333333x + x2 = 0.0 + -7.55

Combine like terms: 0.0 + -7.55 = -7.55
-9.533333333x + x2 = -7.55

The x term is -9.533333333x.  Take half its coefficient (-4.766666667).
Square it (22.72111111) and add it to both sides.

Add '22.72111111' to each side of the equation.
-9.533333333x + 22.72111111 + x2 = -7.55 + 22.72111111

Reorder the terms:
22.72111111 + -9.533333333x + x2 = -7.55 + 22.72111111

Combine like terms: -7.55 + 22.72111111 = 15.17111111
22.72111111 + -9.533333333x + x2 = 15.17111111

Factor a perfect square on the left side:
(x + -4.766666667)(x + -4.766666667) = 15.17111111

Calculate the square root of the right side: 3.895011054

Break this problem into two subproblems by setting 
(x + -4.766666667) equal to 3.895011054 and -3.895011054.

Subproblem 1
x + -4.766666667 = 3.895011054

Simplifying
x + -4.766666667 = 3.895011054

Reorder the terms:
-4.766666667 + x = 3.895011054

Solving
-4.766666667 + x = 3.895011054

Solving for variable 'x'.

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

Add '4.766666667' to each side of the equation.
-4.766666667 + 4.766666667 + x = 3.895011054 + 4.766666667

Combine like terms: -4.766666667 + 4.766666667 = 0.000000000
0.000000000 + x = 3.895011054 + 4.766666667
x = 3.895011054 + 4.766666667

Combine like terms: 3.895011054 + 4.766666667 = 8.661677721
x = 8.661677721

Simplifying
x = 8.661677721

Subproblem 2
x + -4.766666667 = -3.895011054

Simplifying
x + -4.766666667 = -3.895011054

Reorder the terms:
-4.766666667 + x = -3.895011054

Solving
-4.766666667 + x = -3.895011054

Solving for variable 'x'.

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

Add '4.766666667' to each side of the equation.
-4.766666667 + 4.766666667 + x = -3.895011054 + 4.766666667

Combine like terms: -4.766666667 + 4.766666667 = 0.000000000
0.000000000 + x = -3.895011054 + 4.766666667
x = -3.895011054 + 4.766666667

Combine like terms: -3.895011054 + 4.766666667 = 0.871655613
x = 0.871655613

Simplifying
x = 0.871655613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.661677721, 0.871655613}