(6x-147)x=180

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Solution for (6x-147)x=180 equation: 


Simplifying
(6x + -147) * x = 180

Reorder the terms:
(-147 + 6x) * x = 180

Reorder the terms for easier multiplication:
x(-147 + 6x) = 180
(-147 * x + 6x * x) = 180
(-147x + 6x2) = 180

Solving
-147x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -147x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -147x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -49x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + -49x + 2x2)' equal to zero and attempt to solve:

Simplifying
-60 + -49x + 2x2 = 0

Solving
-60 + -49x + 2x2 = 0

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

Divide each side by '2'.
-30 + -24.5x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -24.5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -24.5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -24.5x + x2 = 0 + 30
-24.5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-24.5x + x2 = 30

The x term is -24.5x.  Take half its coefficient (-12.25).
Square it (150.0625) and add it to both sides.

Add '150.0625' to each side of the equation.
-24.5x + 150.0625 + x2 = 30 + 150.0625

Reorder the terms:
150.0625 + -24.5x + x2 = 30 + 150.0625

Combine like terms: 30 + 150.0625 = 180.0625
150.0625 + -24.5x + x2 = 180.0625

Factor a perfect square on the left side:
(x + -12.25)(x + -12.25) = 180.0625

Calculate the square root of the right side: 13.4187369

Break this problem into two subproblems by setting 
(x + -12.25) equal to 13.4187369 and -13.4187369.


Subproblem 1
x + -12.25 = 13.4187369

Simplifying
x + -12.25 = 13.4187369

Reorder the terms:
-12.25 + x = 13.4187369

Solving
-12.25 + x = 13.4187369

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = 13.4187369 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = 13.4187369 + 12.25
x = 13.4187369 + 12.25

Combine like terms: 13.4187369 + 12.25 = 25.6687369
x = 25.6687369

Simplifying
x = 25.6687369


Subproblem 2
x + -12.25 = -13.4187369

Simplifying
x + -12.25 = -13.4187369

Reorder the terms:
-12.25 + x = -13.4187369

Solving
-12.25 + x = -13.4187369

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = -13.4187369 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = -13.4187369 + 12.25
x = -13.4187369 + 12.25

Combine like terms: -13.4187369 + 12.25 = -1.1687369
x = -1.1687369

Simplifying
x = -1.1687369


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.6687369, -1.1687369}
Solution
x = {25.6687369, -1.1687369}

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