3x(95-6x)=x-152

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Solution for 3x(95-6x)=x-152 equation: 


Simplifying
3x(95 + -6x) = x + -152
(95 * 3x + -6x * 3x) = x + -152
(285x + -18x2) = x + -152

Reorder the terms:
285x + -18x2 = -152 + x

Solving
285x + -18x2 = -152 + x

Solving for variable 'x'.

Reorder the terms:
152 + 285x + -1x + -18x2 = -152 + x + 152 + -1x

Combine like terms: 285x + -1x = 284x
152 + 284x + -18x2 = -152 + x + 152 + -1x

Reorder the terms:
152 + 284x + -18x2 = -152 + 152 + x + -1x

Combine like terms: -152 + 152 = 0
152 + 284x + -18x2 = 0 + x + -1x
152 + 284x + -18x2 = x + -1x

Combine like terms: x + -1x = 0
152 + 284x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(76 + 142x + -9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(76 + 142x + -9x2)' equal to zero and attempt to solve:

Simplifying
76 + 142x + -9x2 = 0

Solving
76 + 142x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-8.444444444 + -15.77777778x + x2 = 0

Move the constant term to the right:

Add '8.444444444' to each side of the equation.
-8.444444444 + -15.77777778x + 8.444444444 + x2 = 0 + 8.444444444

Reorder the terms:
-8.444444444 + 8.444444444 + -15.77777778x + x2 = 0 + 8.444444444

Combine like terms: -8.444444444 + 8.444444444 = 0.000000000
0.000000000 + -15.77777778x + x2 = 0 + 8.444444444
-15.77777778x + x2 = 0 + 8.444444444

Combine like terms: 0 + 8.444444444 = 8.444444444
-15.77777778x + x2 = 8.444444444

The x term is -15.77777778x.  Take half its coefficient (-7.88888889).
Square it (62.23456792) and add it to both sides.

Add '62.23456792' to each side of the equation.
-15.77777778x + 62.23456792 + x2 = 8.444444444 + 62.23456792

Reorder the terms:
62.23456792 + -15.77777778x + x2 = 8.444444444 + 62.23456792

Combine like terms: 8.444444444 + 62.23456792 = 70.679012364
62.23456792 + -15.77777778x + x2 = 70.679012364

Factor a perfect square on the left side:
(x + -7.88888889)(x + -7.88888889) = 70.679012364

Calculate the square root of the right side: 8.407081085

Break this problem into two subproblems by setting 
(x + -7.88888889) equal to 8.407081085 and -8.407081085.


Subproblem 1
x + -7.88888889 = 8.407081085

Simplifying
x + -7.88888889 = 8.407081085

Reorder the terms:
-7.88888889 + x = 8.407081085

Solving
-7.88888889 + x = 8.407081085

Solving for variable 'x'.

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

Add '7.88888889' to each side of the equation.
-7.88888889 + 7.88888889 + x = 8.407081085 + 7.88888889

Combine like terms: -7.88888889 + 7.88888889 = 0.00000000
0.00000000 + x = 8.407081085 + 7.88888889
x = 8.407081085 + 7.88888889

Combine like terms: 8.407081085 + 7.88888889 = 16.295969975
x = 16.295969975

Simplifying
x = 16.295969975


Subproblem 2
x + -7.88888889 = -8.407081085

Simplifying
x + -7.88888889 = -8.407081085

Reorder the terms:
-7.88888889 + x = -8.407081085

Solving
-7.88888889 + x = -8.407081085

Solving for variable 'x'.

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

Add '7.88888889' to each side of the equation.
-7.88888889 + 7.88888889 + x = -8.407081085 + 7.88888889

Combine like terms: -7.88888889 + 7.88888889 = 0.00000000
0.00000000 + x = -8.407081085 + 7.88888889
x = -8.407081085 + 7.88888889

Combine like terms: -8.407081085 + 7.88888889 = -0.518192195
x = -0.518192195

Simplifying
x = -0.518192195


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.295969975, -0.518192195}
Solution
x = {16.295969975, -0.518192195}

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