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

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


Simplifying
6x(4x2 + 6x + 5) + -2x(5 + -1x) = 0

Reorder the terms:
6x(5 + 6x + 4x2) + -2x(5 + -1x) = 0
(5 * 6x + 6x * 6x + 4x2 * 6x) + -2x(5 + -1x) = 0
(30x + 36x2 + 24x3) + -2x(5 + -1x) = 0
30x + 36x2 + 24x3 + (5 * -2x + -1x * -2x) = 0
30x + 36x2 + 24x3 + (-10x + 2x2) = 0

Reorder the terms:
30x + -10x + 36x2 + 2x2 + 24x3 = 0

Combine like terms: 30x + -10x = 20x
20x + 36x2 + 2x2 + 24x3 = 0

Combine like terms: 36x2 + 2x2 = 38x2
20x + 38x2 + 24x3 = 0

Solving
20x + 38x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(10 + 19x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + 19x + 12x2)' equal to zero and attempt to solve:

Simplifying
10 + 19x + 12x2 = 0

Solving
10 + 19x + 12x2 = 0

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

Divide each side by '12'.
0.8333333333 + 1.583333333x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 1.583333333x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 1.583333333x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 1.583333333x + x2 = 0 + -0.8333333333
1.583333333x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
1.583333333x + x2 = -0.8333333333

The x term is 1.583333333x.  Take half its coefficient (0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
1.583333333x + 0.6267361108 + x2 = -0.8333333333 + 0.6267361108

Reorder the terms:
0.6267361108 + 1.583333333x + x2 = -0.8333333333 + 0.6267361108

Combine like terms: -0.8333333333 + 0.6267361108 = -0.2065972225
0.6267361108 + 1.583333333x + x2 = -0.2065972225

Factor a perfect square on the left side:
(x + 0.7916666665)(x + 0.7916666665) = -0.2065972225

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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