16*(9x-1)*(1-x)+(4-x)*(74x-8)=48

Solution for 16*(9x-1)*(1-x)+(4-x)*(74x-8)=48 equation:

Simplifying
16(9x + -1)(1 + -1x) + (4 + -1x)(74x + -8) = 48

Reorder the terms:
16(-1 + 9x)(1 + -1x) + (4 + -1x)(74x + -8) = 48

Multiply (-1 + 9x) * (1 + -1x)
16(-1(1 + -1x) + 9x * (1 + -1x)) + (4 + -1x)(74x + -8) = 48
16((1 * -1 + -1x * -1) + 9x * (1 + -1x)) + (4 + -1x)(74x + -8) = 48
16((-1 + 1x) + 9x * (1 + -1x)) + (4 + -1x)(74x + -8) = 48
16(-1 + 1x + (1 * 9x + -1x * 9x)) + (4 + -1x)(74x + -8) = 48
16(-1 + 1x + (9x + -9x2)) + (4 + -1x)(74x + -8) = 48

Combine like terms: 1x + 9x = 10x
16(-1 + 10x + -9x2) + (4 + -1x)(74x + -8) = 48
(-1 * 16 + 10x * 16 + -9x2 * 16) + (4 + -1x)(74x + -8) = 48
(-16 + 160x + -144x2) + (4 + -1x)(74x + -8) = 48

Reorder the terms:
-16 + 160x + -144x2 + (4 + -1x)(-8 + 74x) = 48

Multiply (4 + -1x) * (-8 + 74x)
-16 + 160x + -144x2 + (4(-8 + 74x) + -1x * (-8 + 74x)) = 48
-16 + 160x + -144x2 + ((-8 * 4 + 74x * 4) + -1x * (-8 + 74x)) = 48
-16 + 160x + -144x2 + ((-32 + 296x) + -1x * (-8 + 74x)) = 48
-16 + 160x + -144x2 + (-32 + 296x + (-8 * -1x + 74x * -1x)) = 48
-16 + 160x + -144x2 + (-32 + 296x + (8x + -74x2)) = 48

Combine like terms: 296x + 8x = 304x
-16 + 160x + -144x2 + (-32 + 304x + -74x2) = 48

Reorder the terms:
-16 + -32 + 160x + 304x + -144x2 + -74x2 = 48

Combine like terms: -16 + -32 = -48
-48 + 160x + 304x + -144x2 + -74x2 = 48

Combine like terms: 160x + 304x = 464x
-48 + 464x + -144x2 + -74x2 = 48

Combine like terms: -144x2 + -74x2 = -218x2
-48 + 464x + -218x2 = 48

Solving
-48 + 464x + -218x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + -48 + 464x + -218x2 = 48 + -48

Combine like terms: -48 + -48 = -96
-96 + 464x + -218x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-96 + 464x + -218x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 232x + -109x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-48 + 232x + -109x2)' equal to zero and attempt to solve:

Simplifying
-48 + 232x + -109x2 = 0

Solving
-48 + 232x + -109x2 = 0

Begin completing the square.  Divide all terms by
-109 the coefficient of the squared term: 

Divide each side by '-109'.
0.4403669725 + -2.128440367x + x2 = 0

Move the constant term to the right:

Add '-0.4403669725' to each side of the equation.
0.4403669725 + -2.128440367x + -0.4403669725 + x2 = 0 + -0.4403669725

Reorder the terms:
0.4403669725 + -0.4403669725 + -2.128440367x + x2 = 0 + -0.4403669725

Combine like terms: 0.4403669725 + -0.4403669725 = 0.0000000000
0.0000000000 + -2.128440367x + x2 = 0 + -0.4403669725
-2.128440367x + x2 = 0 + -0.4403669725

Combine like terms: 0 + -0.4403669725 = -0.4403669725
-2.128440367x + x2 = -0.4403669725

The x term is -2.128440367x.  Take half its coefficient (-1.064220184).
Square it (1.132564600) and add it to both sides.

Add '1.132564600' to each side of the equation.
-2.128440367x + 1.132564600 + x2 = -0.4403669725 + 1.132564600

Reorder the terms:
1.132564600 + -2.128440367x + x2 = -0.4403669725 + 1.132564600

Combine like terms: -0.4403669725 + 1.132564600 = 0.6921976275
1.132564600 + -2.128440367x + x2 = 0.6921976275

Factor a perfect square on the left side:
(x + -1.064220184)(x + -1.064220184) = 0.6921976275

Calculate the square root of the right side: 0.831984151

Break this problem into two subproblems by setting 
(x + -1.064220184) equal to 0.831984151 and -0.831984151.

Subproblem 1
x + -1.064220184 = 0.831984151

Simplifying
x + -1.064220184 = 0.831984151

Reorder the terms:
-1.064220184 + x = 0.831984151

Solving
-1.064220184 + x = 0.831984151

Solving for variable 'x'.

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

Add '1.064220184' to each side of the equation.
-1.064220184 + 1.064220184 + x = 0.831984151 + 1.064220184

Combine like terms: -1.064220184 + 1.064220184 = 0.000000000
0.000000000 + x = 0.831984151 + 1.064220184
x = 0.831984151 + 1.064220184

Combine like terms: 0.831984151 + 1.064220184 = 1.896204335
x = 1.896204335

Simplifying
x = 1.896204335

Subproblem 2
x + -1.064220184 = -0.831984151

Simplifying
x + -1.064220184 = -0.831984151

Reorder the terms:
-1.064220184 + x = -0.831984151

Solving
-1.064220184 + x = -0.831984151

Solving for variable 'x'.

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

Add '1.064220184' to each side of the equation.
-1.064220184 + 1.064220184 + x = -0.831984151 + 1.064220184

Combine like terms: -1.064220184 + 1.064220184 = 0.000000000
0.000000000 + x = -0.831984151 + 1.064220184
x = -0.831984151 + 1.064220184

Combine like terms: -0.831984151 + 1.064220184 = 0.232236033
x = 0.232236033

Simplifying
x = 0.232236033

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.896204335, 0.232236033}
Solution
x = {1.896204335, 0.232236033}