4x(5-2x)=6

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


Simplifying
4x(5 + -2x) = 6
(5 * 4x + -2x * 4x) = 6
(20x + -8x2) = 6

Solving
20x + -8x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 20x + -8x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 20x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 10x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + 10x + -4x2)' equal to zero and attempt to solve:

Simplifying
-3 + 10x + -4x2 = 0

Solving
-3 + 10x + -4x2 = 0

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

Divide each side by '-4'.
0.75 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.5x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.5x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.5x + x2 = 0 + -0.75
-2.5x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.5x + x2 = -0.75

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -0.75 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.75 + 1.5625

Combine like terms: -0.75 + 1.5625 = 0.8125
1.5625 + -2.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.901387819 and -0.901387819.


Subproblem 1
x + -1.25 = 0.901387819

Simplifying
x + -1.25 = 0.901387819

Reorder the terms:
-1.25 + x = 0.901387819

Solving
-1.25 + x = 0.901387819

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 0.901387819 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 0.901387819 + 1.25
x = 0.901387819 + 1.25

Combine like terms: 0.901387819 + 1.25 = 2.151387819
x = 2.151387819

Simplifying
x = 2.151387819


Subproblem 2
x + -1.25 = -0.901387819

Simplifying
x + -1.25 = -0.901387819

Reorder the terms:
-1.25 + x = -0.901387819

Solving
-1.25 + x = -0.901387819

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -0.901387819 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -0.901387819 + 1.25
x = -0.901387819 + 1.25

Combine like terms: -0.901387819 + 1.25 = 0.348612181
x = 0.348612181

Simplifying
x = 0.348612181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.151387819, 0.348612181}
Solution
x = {2.151387819, 0.348612181}

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