-10+34x=3x(4x-16)

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Solution for -10+34x=3x(4x-16) equation:


Simplifying
-10 + 34x = 3x(4x + -16)

Reorder the terms:
-10 + 34x = 3x(-16 + 4x)
-10 + 34x = (-16 * 3x + 4x * 3x)
-10 + 34x = (-48x + 12x2)

Solving
-10 + 34x = -48x + 12x2

Solving for variable 'x'.

Combine like terms: 34x + 48x = 82x
-10 + 82x + -12x2 = -48x + 12x2 + 48x + -12x2

Reorder the terms:
-10 + 82x + -12x2 = -48x + 48x + 12x2 + -12x2

Combine like terms: -48x + 48x = 0
-10 + 82x + -12x2 = 0 + 12x2 + -12x2
-10 + 82x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-10 + 82x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 41x + -6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 41x + -6x2)' equal to zero and attempt to solve:

Simplifying
-5 + 41x + -6x2 = 0

Solving
-5 + 41x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.8333333333 + -6.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -6.833333333x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -6.833333333x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -6.833333333x + x2 = 0 + -0.8333333333
-6.833333333x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-6.833333333x + x2 = -0.8333333333

The x term is -6.833333333x.  Take half its coefficient (-3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
-6.833333333x + 11.67361111 + x2 = -0.8333333333 + 11.67361111

Reorder the terms:
11.67361111 + -6.833333333x + x2 = -0.8333333333 + 11.67361111

Combine like terms: -0.8333333333 + 11.67361111 = 10.8402777767
11.67361111 + -6.833333333x + x2 = 10.8402777767

Factor a perfect square on the left side:
(x + -3.416666667)(x + -3.416666667) = 10.8402777767

Calculate the square root of the right side: 3.292457711

Break this problem into two subproblems by setting 
(x + -3.416666667) equal to 3.292457711 and -3.292457711.


Subproblem 1
x + -3.416666667 = 3.292457711

Simplifying
x + -3.416666667 = 3.292457711

Reorder the terms:
-3.416666667 + x = 3.292457711

Solving
-3.416666667 + x = 3.292457711

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = 3.292457711 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = 3.292457711 + 3.416666667
x = 3.292457711 + 3.416666667

Combine like terms: 3.292457711 + 3.416666667 = 6.709124378
x = 6.709124378

Simplifying
x = 6.709124378


Subproblem 2
x + -3.416666667 = -3.292457711

Simplifying
x + -3.416666667 = -3.292457711

Reorder the terms:
-3.416666667 + x = -3.292457711

Solving
-3.416666667 + x = -3.292457711

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = -3.292457711 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = -3.292457711 + 3.416666667
x = -3.292457711 + 3.416666667

Combine like terms: -3.292457711 + 3.416666667 = 0.124208956
x = 0.124208956

Simplifying
x = 0.124208956


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.709124378, 0.124208956}
Solution
x = {6.709124378, 0.124208956}

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