16*(9x-1)*(x-1)-(x-4)*(74x-8)=3*16

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Solution for 16*(9x-1)*(x-1)-(x-4)*(74x-8)=3*16 equation: 


Simplifying
16(9x + -1)(x + -1) + -1(x + -4)(74x + -8) = 3 * 16

Reorder the terms:
16(-1 + 9x)(x + -1) + -1(x + -4)(74x + -8) = 3 * 16

Reorder the terms:
16(-1 + 9x)(-1 + x) + -1(x + -4)(74x + -8) = 3 * 16

Multiply (-1 + 9x) * (-1 + x)
16(-1(-1 + x) + 9x * (-1 + x)) + -1(x + -4)(74x + -8) = 3 * 16
16((-1 * -1 + x * -1) + 9x * (-1 + x)) + -1(x + -4)(74x + -8) = 3 * 16
16((1 + -1x) + 9x * (-1 + x)) + -1(x + -4)(74x + -8) = 3 * 16
16(1 + -1x + (-1 * 9x + x * 9x)) + -1(x + -4)(74x + -8) = 3 * 16
16(1 + -1x + (-9x + 9x2)) + -1(x + -4)(74x + -8) = 3 * 16

Combine like terms: -1x + -9x = -10x
16(1 + -10x + 9x2) + -1(x + -4)(74x + -8) = 3 * 16
(1 * 16 + -10x * 16 + 9x2 * 16) + -1(x + -4)(74x + -8) = 3 * 16
(16 + -160x + 144x2) + -1(x + -4)(74x + -8) = 3 * 16

Reorder the terms:
16 + -160x + 144x2 + -1(-4 + x)(74x + -8) = 3 * 16

Reorder the terms:
16 + -160x + 144x2 + -1(-4 + x)(-8 + 74x) = 3 * 16

Multiply (-4 + x) * (-8 + 74x)
16 + -160x + 144x2 + -1(-4(-8 + 74x) + x(-8 + 74x)) = 3 * 16
16 + -160x + 144x2 + -1((-8 * -4 + 74x * -4) + x(-8 + 74x)) = 3 * 16
16 + -160x + 144x2 + -1((32 + -296x) + x(-8 + 74x)) = 3 * 16
16 + -160x + 144x2 + -1(32 + -296x + (-8 * x + 74x * x)) = 3 * 16
16 + -160x + 144x2 + -1(32 + -296x + (-8x + 74x2)) = 3 * 16

Combine like terms: -296x + -8x = -304x
16 + -160x + 144x2 + -1(32 + -304x + 74x2) = 3 * 16
16 + -160x + 144x2 + (32 * -1 + -304x * -1 + 74x2 * -1) = 3 * 16
16 + -160x + 144x2 + (-32 + 304x + -74x2) = 3 * 16

Reorder the terms:
16 + -32 + -160x + 304x + 144x2 + -74x2 = 3 * 16

Combine like terms: 16 + -32 = -16
-16 + -160x + 304x + 144x2 + -74x2 = 3 * 16

Combine like terms: -160x + 304x = 144x
-16 + 144x + 144x2 + -74x2 = 3 * 16

Combine like terms: 144x2 + -74x2 = 70x2
-16 + 144x + 70x2 = 3 * 16

Multiply 3 * 16
-16 + 144x + 70x2 = 48

Solving
-16 + 144x + 70x2 = 48

Solving for variable 'x'.

Reorder the terms:
-16 + -48 + 144x + 70x2 = 48 + -48

Combine like terms: -16 + -48 = -64
-64 + 144x + 70x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-64 + 144x + 70x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 72x + 35x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + 72x + 35x2)' equal to zero and attempt to solve:

Simplifying
-32 + 72x + 35x2 = 0

Solving
-32 + 72x + 35x2 = 0

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

Divide each side by '35'.
-0.9142857143 + 2.057142857x + x2 = 0

Move the constant term to the right:

Add '0.9142857143' to each side of the equation.
-0.9142857143 + 2.057142857x + 0.9142857143 + x2 = 0 + 0.9142857143

Reorder the terms:
-0.9142857143 + 0.9142857143 + 2.057142857x + x2 = 0 + 0.9142857143

Combine like terms: -0.9142857143 + 0.9142857143 = 0.0000000000
0.0000000000 + 2.057142857x + x2 = 0 + 0.9142857143
2.057142857x + x2 = 0 + 0.9142857143

Combine like terms: 0 + 0.9142857143 = 0.9142857143
2.057142857x + x2 = 0.9142857143

The x term is 2.057142857x.  Take half its coefficient (1.028571429).
Square it (1.057959185) and add it to both sides.

Add '1.057959185' to each side of the equation.
2.057142857x + 1.057959185 + x2 = 0.9142857143 + 1.057959185

Reorder the terms:
1.057959185 + 2.057142857x + x2 = 0.9142857143 + 1.057959185

Combine like terms: 0.9142857143 + 1.057959185 = 1.9722448993
1.057959185 + 2.057142857x + x2 = 1.9722448993

Factor a perfect square on the left side:
(x + 1.028571429)(x + 1.028571429) = 1.9722448993

Calculate the square root of the right side: 1.404366369

Break this problem into two subproblems by setting 
(x + 1.028571429) equal to 1.404366369 and -1.404366369.


Subproblem 1
x + 1.028571429 = 1.404366369

Simplifying
x + 1.028571429 = 1.404366369

Reorder the terms:
1.028571429 + x = 1.404366369

Solving
1.028571429 + x = 1.404366369

Solving for variable 'x'.

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

Add '-1.028571429' to each side of the equation.
1.028571429 + -1.028571429 + x = 1.404366369 + -1.028571429

Combine like terms: 1.028571429 + -1.028571429 = 0.000000000
0.000000000 + x = 1.404366369 + -1.028571429
x = 1.404366369 + -1.028571429

Combine like terms: 1.404366369 + -1.028571429 = 0.37579494
x = 0.37579494

Simplifying
x = 0.37579494


Subproblem 2
x + 1.028571429 = -1.404366369

Simplifying
x + 1.028571429 = -1.404366369

Reorder the terms:
1.028571429 + x = -1.404366369

Solving
1.028571429 + x = -1.404366369

Solving for variable 'x'.

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

Add '-1.028571429' to each side of the equation.
1.028571429 + -1.028571429 + x = -1.404366369 + -1.028571429

Combine like terms: 1.028571429 + -1.028571429 = 0.000000000
0.000000000 + x = -1.404366369 + -1.028571429
x = -1.404366369 + -1.028571429

Combine like terms: -1.404366369 + -1.028571429 = -2.432937798
x = -2.432937798

Simplifying
x = -2.432937798


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37579494, -2.432937798}
Solution
x = {0.37579494, -2.432937798}

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