6x-8=4x(-2x+5)

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Solution for 6x-8=4x(-2x+5) equation: 


Simplifying
6x + -8 = 4x(-2x + 5)

Reorder the terms:
-8 + 6x = 4x(-2x + 5)

Reorder the terms:
-8 + 6x = 4x(5 + -2x)
-8 + 6x = (5 * 4x + -2x * 4x)
-8 + 6x = (20x + -8x2)

Solving
-8 + 6x = 20x + -8x2

Solving for variable 'x'.

Combine like terms: 6x + -20x = -14x
-8 + -14x + 8x2 = 20x + -8x2 + -20x + 8x2

Reorder the terms:
-8 + -14x + 8x2 = 20x + -20x + -8x2 + 8x2

Combine like terms: 20x + -20x = 0
-8 + -14x + 8x2 = 0 + -8x2 + 8x2
-8 + -14x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-8 + -14x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -7x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-4 + -7x + 4x2 = 0

Solving
-4 + -7x + 4x2 = 0

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

Divide each side by '4'.
-1 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.75x + x2 = 0 + 1
-1.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.75x + x2 = 1

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1 + 0.765625

Combine like terms: 1 + 0.765625 = 1.765625
0.765625 + -1.75x + x2 = 1.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.328768227 and -1.328768227.


Subproblem 1
x + -0.875 = 1.328768227

Simplifying
x + -0.875 = 1.328768227

Reorder the terms:
-0.875 + x = 1.328768227

Solving
-0.875 + x = 1.328768227

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.328768227 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.328768227 + 0.875
x = 1.328768227 + 0.875

Combine like terms: 1.328768227 + 0.875 = 2.203768227
x = 2.203768227

Simplifying
x = 2.203768227


Subproblem 2
x + -0.875 = -1.328768227

Simplifying
x + -0.875 = -1.328768227

Reorder the terms:
-0.875 + x = -1.328768227

Solving
-0.875 + x = -1.328768227

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.328768227 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.328768227 + 0.875
x = -1.328768227 + 0.875

Combine like terms: -1.328768227 + 0.875 = -0.453768227
x = -0.453768227

Simplifying
x = -0.453768227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.203768227, -0.453768227}
Solution
x = {2.203768227, -0.453768227}

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