-3x(x-10)=57

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Solution for -3x(x-10)=57 equation: 


Simplifying
-3x(x + -10) = 57

Reorder the terms:
-3x(-10 + x) = 57
(-10 * -3x + x * -3x) = 57
(30x + -3x2) = 57

Solving
30x + -3x2 = 57

Solving for variable 'x'.

Reorder the terms:
-57 + 30x + -3x2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + 30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + 10x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-19 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
-19 + 10x + -1x2 = 0

Solving
-19 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
19 + -10x + x2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -10x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + -10x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -10x + x2 = 0 + -19
-10x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-10x + x2 = -19

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -19 + 25

Reorder the terms:
25 + -10x + x2 = -19 + 25

Combine like terms: -19 + 25 = 6
25 + -10x + x2 = 6

Factor a perfect square on the left side:
(x + -5)(x + -5) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -5) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -5 = 2.449489743

Simplifying
x + -5 = 2.449489743

Reorder the terms:
-5 + x = 2.449489743

Solving
-5 + x = 2.449489743

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2.449489743 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.449489743 + 5
x = 2.449489743 + 5

Combine like terms: 2.449489743 + 5 = 7.449489743
x = 7.449489743

Simplifying
x = 7.449489743


Subproblem 2
x + -5 = -2.449489743

Simplifying
x + -5 = -2.449489743

Reorder the terms:
-5 + x = -2.449489743

Solving
-5 + x = -2.449489743

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2.449489743 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.449489743 + 5
x = -2.449489743 + 5

Combine like terms: -2.449489743 + 5 = 2.550510257
x = 2.550510257

Simplifying
x = 2.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.449489743, 2.550510257}
Solution
x = {7.449489743, 2.550510257}

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