8x+2=7x(x-4)+5

Solution for 8x+2=7x(x-4)+5 equation:

Simplifying
8x + 2 = 7x(x + -4) + 5

Reorder the terms:
2 + 8x = 7x(x + -4) + 5

Reorder the terms:
2 + 8x = 7x(-4 + x) + 5
2 + 8x = (-4 * 7x + x * 7x) + 5
2 + 8x = (-28x + 7x2) + 5

Reorder the terms:
2 + 8x = 5 + -28x + 7x2

Solving
2 + 8x = 5 + -28x + 7x2

Solving for variable 'x'.

Reorder the terms:
2 + -5 + 8x + 28x + -7x2 = 5 + -28x + 7x2 + -5 + 28x + -7x2

Combine like terms: 2 + -5 = -3
-3 + 8x + 28x + -7x2 = 5 + -28x + 7x2 + -5 + 28x + -7x2

Combine like terms: 8x + 28x = 36x
-3 + 36x + -7x2 = 5 + -28x + 7x2 + -5 + 28x + -7x2

Reorder the terms:
-3 + 36x + -7x2 = 5 + -5 + -28x + 28x + 7x2 + -7x2

Combine like terms: 5 + -5 = 0
-3 + 36x + -7x2 = 0 + -28x + 28x + 7x2 + -7x2
-3 + 36x + -7x2 = -28x + 28x + 7x2 + -7x2

Combine like terms: -28x + 28x = 0
-3 + 36x + -7x2 = 0 + 7x2 + -7x2
-3 + 36x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-3 + 36x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.4285714286 + -5.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -5.142857143x + -0.4285714286 + x2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + -5.142857143x + x2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + -5.142857143x + x2 = 0 + -0.4285714286
-5.142857143x + x2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
-5.142857143x + x2 = -0.4285714286

The x term is -5.142857143x.  Take half its coefficient (-2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
-5.142857143x + 6.612244901 + x2 = -0.4285714286 + 6.612244901

Reorder the terms:
6.612244901 + -5.142857143x + x2 = -0.4285714286 + 6.612244901

Combine like terms: -0.4285714286 + 6.612244901 = 6.1836734724
6.612244901 + -5.142857143x + x2 = 6.1836734724

Factor a perfect square on the left side:
(x + -2.571428572)(x + -2.571428572) = 6.1836734724

Calculate the square root of the right side: 2.486699313

Break this problem into two subproblems by setting 
(x + -2.571428572) equal to 2.486699313 and -2.486699313.

Subproblem 1
x + -2.571428572 = 2.486699313

Simplifying
x + -2.571428572 = 2.486699313

Reorder the terms:
-2.571428572 + x = 2.486699313

Solving
-2.571428572 + x = 2.486699313

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = 2.486699313 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = 2.486699313 + 2.571428572
x = 2.486699313 + 2.571428572

Combine like terms: 2.486699313 + 2.571428572 = 5.058127885
x = 5.058127885

Simplifying
x = 5.058127885

Subproblem 2
x + -2.571428572 = -2.486699313

Simplifying
x + -2.571428572 = -2.486699313

Reorder the terms:
-2.571428572 + x = -2.486699313

Solving
-2.571428572 + x = -2.486699313

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = -2.486699313 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = -2.486699313 + 2.571428572
x = -2.486699313 + 2.571428572

Combine like terms: -2.486699313 + 2.571428572 = 0.084729259
x = 0.084729259

Simplifying
x = 0.084729259

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.058127885, 0.084729259}