2x(3x-10)=90

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Solution for 2x(3x-10)=90 equation: 


Simplifying
2x(3x + -10) = 90

Reorder the terms:
2x(-10 + 3x) = 90
(-10 * 2x + 3x * 2x) = 90
(-20x + 6x2) = 90

Solving
-20x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -20x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -10x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
-45 + -10x + 3x2 = 0

Solving
-45 + -10x + 3x2 = 0

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

Divide each side by '3'.
-15 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -3.333333333x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -3.333333333x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -3.333333333x + x2 = 0 + 15
-3.333333333x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-3.333333333x + x2 = 15

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 15 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 15 + 2.777777779

Combine like terms: 15 + 2.777777779 = 17.777777779
2.777777779 + -3.333333333x + x2 = 17.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 17.777777779

Calculate the square root of the right side: 4.216370214

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 4.216370214 and -4.216370214.


Subproblem 1
x + -1.666666667 = 4.216370214

Simplifying
x + -1.666666667 = 4.216370214

Reorder the terms:
-1.666666667 + x = 4.216370214

Solving
-1.666666667 + x = 4.216370214

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 4.216370214 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 4.216370214 + 1.666666667
x = 4.216370214 + 1.666666667

Combine like terms: 4.216370214 + 1.666666667 = 5.883036881
x = 5.883036881

Simplifying
x = 5.883036881


Subproblem 2
x + -1.666666667 = -4.216370214

Simplifying
x + -1.666666667 = -4.216370214

Reorder the terms:
-1.666666667 + x = -4.216370214

Solving
-1.666666667 + x = -4.216370214

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -4.216370214 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -4.216370214 + 1.666666667
x = -4.216370214 + 1.666666667

Combine like terms: -4.216370214 + 1.666666667 = -2.549703547
x = -2.549703547

Simplifying
x = -2.549703547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.883036881, -2.549703547}
Solution
x = {5.883036881, -2.549703547}

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