5(2x^2-2)-2x(x-3)=

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Solution for 5(2x^2-2)-2x(x-3)= equation: 


Simplifying
5(2x2 + -2) + -2x(x + -3) = 0

Reorder the terms:
5(-2 + 2x2) + -2x(x + -3) = 0
(-2 * 5 + 2x2 * 5) + -2x(x + -3) = 0
(-10 + 10x2) + -2x(x + -3) = 0

Reorder the terms:
-10 + 10x2 + -2x(-3 + x) = 0
-10 + 10x2 + (-3 * -2x + x * -2x) = 0
-10 + 10x2 + (6x + -2x2) = 0

Reorder the terms:
-10 + 6x + 10x2 + -2x2 = 0

Combine like terms: 10x2 + -2x2 = 8x2
-10 + 6x + 8x2 = 0

Solving
-10 + 6x + 8x2 = 0

Solving for variable 'x'.

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 = 0.804247642
x = 0.804247642

Simplifying
x = 0.804247642


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 = -1.554247642
x = -1.554247642

Simplifying
x = -1.554247642


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

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