21x+8x(-2x+11)=4x+(-6x-3x+2)

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Solution for 21x+8x(-2x+11)=4x+(-6x-3x+2) equation: 


Simplifying
21x + 8x(-2x + 11) = 4x + (-6x + -3x + 2)

Reorder the terms:
21x + 8x(11 + -2x) = 4x + (-6x + -3x + 2)
21x + (11 * 8x + -2x * 8x) = 4x + (-6x + -3x + 2)
21x + (88x + -16x2) = 4x + (-6x + -3x + 2)

Combine like terms: 21x + 88x = 109x
109x + -16x2 = 4x + (-6x + -3x + 2)

Reorder the terms:
109x + -16x2 = 4x + (2 + -6x + -3x)

Combine like terms: -6x + -3x = -9x
109x + -16x2 = 4x + (2 + -9x)

Remove parenthesis around (2 + -9x)
109x + -16x2 = 4x + 2 + -9x

Reorder the terms:
109x + -16x2 = 2 + 4x + -9x

Combine like terms: 4x + -9x = -5x
109x + -16x2 = 2 + -5x

Solving
109x + -16x2 = 2 + -5x

Solving for variable 'x'.

Reorder the terms:
-2 + 109x + 5x + -16x2 = 2 + -5x + -2 + 5x

Combine like terms: 109x + 5x = 114x
-2 + 114x + -16x2 = 2 + -5x + -2 + 5x

Reorder the terms:
-2 + 114x + -16x2 = 2 + -2 + -5x + 5x

Combine like terms: 2 + -2 = 0
-2 + 114x + -16x2 = 0 + -5x + 5x
-2 + 114x + -16x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-2 + 114x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 57x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 57x + -8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 57x + -8x2 = 0

Solving
-1 + 57x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -7.125x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -7.125x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -7.125x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -7.125x + x2 = 0 + -0.125
-7.125x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-7.125x + x2 = -0.125

The x term is -7.125x.  Take half its coefficient (-3.5625).
Square it (12.69140625) and add it to both sides.

Add '12.69140625' to each side of the equation.
-7.125x + 12.69140625 + x2 = -0.125 + 12.69140625

Reorder the terms:
12.69140625 + -7.125x + x2 = -0.125 + 12.69140625

Combine like terms: -0.125 + 12.69140625 = 12.56640625
12.69140625 + -7.125x + x2 = 12.56640625

Factor a perfect square on the left side:
(x + -3.5625)(x + -3.5625) = 12.56640625

Calculate the square root of the right side: 3.544912728

Break this problem into two subproblems by setting 
(x + -3.5625) equal to 3.544912728 and -3.544912728.


Subproblem 1
x + -3.5625 = 3.544912728

Simplifying
x + -3.5625 = 3.544912728

Reorder the terms:
-3.5625 + x = 3.544912728

Solving
-3.5625 + x = 3.544912728

Solving for variable 'x'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + x = 3.544912728 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + x = 3.544912728 + 3.5625
x = 3.544912728 + 3.5625

Combine like terms: 3.544912728 + 3.5625 = 7.107412728
x = 7.107412728

Simplifying
x = 7.107412728


Subproblem 2
x + -3.5625 = -3.544912728

Simplifying
x + -3.5625 = -3.544912728

Reorder the terms:
-3.5625 + x = -3.544912728

Solving
-3.5625 + x = -3.544912728

Solving for variable 'x'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + x = -3.544912728 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + x = -3.544912728 + 3.5625
x = -3.544912728 + 3.5625

Combine like terms: -3.544912728 + 3.5625 = 0.017587272
x = 0.017587272

Simplifying
x = 0.017587272


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.107412728, 0.017587272}
Solution
x = {7.107412728, 0.017587272}

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