2x(4x-3)=10

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Solution for 2x(4x-3)=10 equation: 


Simplifying
2x(4x + -3) = 10

Reorder the terms:
2x(-3 + 4x) = 10
(-3 * 2x + 4x * 2x) = 10
(-6x + 8x2) = 10

Solving
-6x + 8x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -6x + 8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -6x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -3x + 4x2 = 0

Solving
-5 + -3x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.75x + x2 = 0 + 1.25
-0.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.75x + x2 = 1.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + -0.75x + x2 = 1.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.179247642 and -1.179247642.


Subproblem 1
x + -0.375 = 1.179247642

Simplifying
x + -0.375 = 1.179247642

Reorder the terms:
-0.375 + x = 1.179247642

Solving
-0.375 + x = 1.179247642

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.179247642 + 0.375
x = 1.179247642 + 0.375

Combine like terms: 1.179247642 + 0.375 = 1.554247642
x = 1.554247642

Simplifying
x = 1.554247642


Subproblem 2
x + -0.375 = -1.179247642

Simplifying
x + -0.375 = -1.179247642

Reorder the terms:
-0.375 + x = -1.179247642

Solving
-0.375 + x = -1.179247642

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.179247642 + 0.375
x = -1.179247642 + 0.375

Combine like terms: -1.179247642 + 0.375 = -0.804247642
x = -0.804247642

Simplifying
x = -0.804247642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.554247642, -0.804247642}
Solution
x = {1.554247642, -0.804247642}

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