10=(2x-1)*4x

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Solution for 10=(2x-1)*4x equation:


Simplifying
10 = (2x + -1) * 4x

Reorder the terms:
10 = (-1 + 2x) * 4x

Reorder the terms for easier multiplication:
10 = 4x(-1 + 2x)
10 = (-1 * 4x + 2x * 4x)
10 = (-4x + 8x2)

Solving
10 = -4x + 8x2

Solving for variable 'x'.

Reorder the terms:
10 + 4x + -8x2 = -4x + 4x + 8x2 + -8x2

Combine like terms: -4x + 4x = 0
10 + 4x + -8x2 = 0 + 8x2 + -8x2
10 + 4x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
10 + 4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 2x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 2x + -4x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x + -4x2 = 0

Solving
5 + 2x + -4x2 = 0

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

Divide each side by '-4'.
-1.25 + -0.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.5x + x2 = 0 + 1.25
-0.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.5x + x2 = 1.25

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + -0.5x + x2 = 1.3125

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.145643924 and -1.145643924.


Subproblem 1
x + -0.25 = 1.145643924

Simplifying
x + -0.25 = 1.145643924

Reorder the terms:
-0.25 + x = 1.145643924

Solving
-0.25 + x = 1.145643924

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.145643924 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.145643924 + 0.25
x = 1.145643924 + 0.25

Combine like terms: 1.145643924 + 0.25 = 1.395643924
x = 1.395643924

Simplifying
x = 1.395643924


Subproblem 2
x + -0.25 = -1.145643924

Simplifying
x + -0.25 = -1.145643924

Reorder the terms:
-0.25 + x = -1.145643924

Solving
-0.25 + x = -1.145643924

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.145643924 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.145643924 + 0.25
x = -1.145643924 + 0.25

Combine like terms: -1.145643924 + 0.25 = -0.895643924
x = -0.895643924

Simplifying
x = -0.895643924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.395643924, -0.895643924}
Solution
x = {1.395643924, -0.895643924}

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