(x^2-7x)(7-3)=4x+14

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Solution for (x^2-7x)(7-3)=4x+14 equation: 


Simplifying
(x2 + -7x)(7 + -3) = 4x + 14

Reorder the terms:
(-7x + x2)(7 + -3) = 4x + 14

Combine like terms: 7 + -3 = 4
(-7x + x2)(4) = 4x + 14

Reorder the terms for easier multiplication:
4(-7x + x2) = 4x + 14
(-7x * 4 + x2 * 4) = 4x + 14
(-28x + 4x2) = 4x + 14

Reorder the terms:
-28x + 4x2 = 14 + 4x

Solving
-28x + 4x2 = 14 + 4x

Solving for variable 'x'.

Reorder the terms:
-14 + -28x + -4x + 4x2 = 14 + 4x + -14 + -4x

Combine like terms: -28x + -4x = -32x
-14 + -32x + 4x2 = 14 + 4x + -14 + -4x

Reorder the terms:
-14 + -32x + 4x2 = 14 + -14 + 4x + -4x

Combine like terms: 14 + -14 = 0
-14 + -32x + 4x2 = 0 + 4x + -4x
-14 + -32x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-14 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -16x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -16x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + -16x + 2x2 = 0

Solving
-7 + -16x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -8x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -8x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -8x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -8x + x2 = 0 + 3.5
-8x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-8x + x2 = 3.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 3.5 + 16

Reorder the terms:
16 + -8x + x2 = 3.5 + 16

Combine like terms: 3.5 + 16 = 19.5
16 + -8x + x2 = 19.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(x + -4) equal to 4.415880433 and -4.415880433.


Subproblem 1
x + -4 = 4.415880433

Simplifying
x + -4 = 4.415880433

Reorder the terms:
-4 + x = 4.415880433

Solving
-4 + x = 4.415880433

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.415880433 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.415880433 + 4
x = 4.415880433 + 4

Combine like terms: 4.415880433 + 4 = 8.415880433
x = 8.415880433

Simplifying
x = 8.415880433


Subproblem 2
x + -4 = -4.415880433

Simplifying
x + -4 = -4.415880433

Reorder the terms:
-4 + x = -4.415880433

Solving
-4 + x = -4.415880433

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.415880433 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.415880433 + 4
x = -4.415880433 + 4

Combine like terms: -4.415880433 + 4 = -0.415880433
x = -0.415880433

Simplifying
x = -0.415880433


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.415880433, -0.415880433}
Solution
x = {8.415880433, -0.415880433}

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