(6x-10)(3x+1)=180

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Solution for (6x-10)(3x+1)=180 equation: 


Simplifying
(6x + -10)(3x + 1) = 180

Reorder the terms:
(-10 + 6x)(3x + 1) = 180

Reorder the terms:
(-10 + 6x)(1 + 3x) = 180

Multiply (-10 + 6x) * (1 + 3x)
(-10(1 + 3x) + 6x * (1 + 3x)) = 180
((1 * -10 + 3x * -10) + 6x * (1 + 3x)) = 180
((-10 + -30x) + 6x * (1 + 3x)) = 180
(-10 + -30x + (1 * 6x + 3x * 6x)) = 180
(-10 + -30x + (6x + 18x2)) = 180

Combine like terms: -30x + 6x = -24x
(-10 + -24x + 18x2) = 180

Solving
-10 + -24x + 18x2 = 180

Solving for variable 'x'.

Reorder the terms:
-10 + -180 + -24x + 18x2 = 180 + -180

Combine like terms: -10 + -180 = -190
-190 + -24x + 18x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-190 + -24x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-95 + -12x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-95 + -12x + 9x2)' equal to zero and attempt to solve:

Simplifying
-95 + -12x + 9x2 = 0

Solving
-95 + -12x + 9x2 = 0

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

Divide each side by '9'.
-10.55555556 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '10.55555556' to each side of the equation.
-10.55555556 + -1.333333333x + 10.55555556 + x2 = 0 + 10.55555556

Reorder the terms:
-10.55555556 + 10.55555556 + -1.333333333x + x2 = 0 + 10.55555556

Combine like terms: -10.55555556 + 10.55555556 = 0.00000000
0.00000000 + -1.333333333x + x2 = 0 + 10.55555556
-1.333333333x + x2 = 0 + 10.55555556

Combine like terms: 0 + 10.55555556 = 10.55555556
-1.333333333x + x2 = 10.55555556

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 10.55555556 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 10.55555556 + 0.4444444442

Combine like terms: 10.55555556 + 0.4444444442 = 11.0000000042
0.4444444442 + -1.333333333x + x2 = 11.0000000042

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 11.0000000042

Calculate the square root of the right side: 3.316624791

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 3.316624791 and -3.316624791.


Subproblem 1
x + -0.6666666665 = 3.316624791

Simplifying
x + -0.6666666665 = 3.316624791

Reorder the terms:
-0.6666666665 + x = 3.316624791

Solving
-0.6666666665 + x = 3.316624791

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 3.316624791 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 3.316624791 + 0.6666666665
x = 3.316624791 + 0.6666666665

Combine like terms: 3.316624791 + 0.6666666665 = 3.9832914575
x = 3.9832914575

Simplifying
x = 3.9832914575


Subproblem 2
x + -0.6666666665 = -3.316624791

Simplifying
x + -0.6666666665 = -3.316624791

Reorder the terms:
-0.6666666665 + x = -3.316624791

Solving
-0.6666666665 + x = -3.316624791

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -3.316624791 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -3.316624791 + 0.6666666665
x = -3.316624791 + 0.6666666665

Combine like terms: -3.316624791 + 0.6666666665 = -2.6499581245
x = -2.6499581245

Simplifying
x = -2.6499581245


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.9832914575, -2.6499581245}
Solution
x = {3.9832914575, -2.6499581245}

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