2x(5x-6)=180

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Solution for 2x(5x-6)=180 equation: 


Simplifying
2x(5x + -6) = 180

Reorder the terms:
2x(-6 + 5x) = 180
(-6 * 2x + 5x * 2x) = 180
(-12x + 10x2) = 180

Solving
-12x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -12x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -12x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -6x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-90 + -6x + 5x2 = 0

Solving
-90 + -6x + 5x2 = 0

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

Divide each side by '5'.
-18 + -1.2x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1.2x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -1.2x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1.2x + x2 = 0 + 18
-1.2x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1.2x + x2 = 18

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 18 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 18 + 0.36

Combine like terms: 18 + 0.36 = 18.36
0.36 + -1.2x + x2 = 18.36

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 18.36

Calculate the square root of the right side: 4.284857057

Break this problem into two subproblems by setting 
(x + -0.6) equal to 4.284857057 and -4.284857057.


Subproblem 1
x + -0.6 = 4.284857057

Simplifying
x + -0.6 = 4.284857057

Reorder the terms:
-0.6 + x = 4.284857057

Solving
-0.6 + x = 4.284857057

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 4.284857057 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 4.284857057 + 0.6
x = 4.284857057 + 0.6

Combine like terms: 4.284857057 + 0.6 = 4.884857057
x = 4.884857057

Simplifying
x = 4.884857057


Subproblem 2
x + -0.6 = -4.284857057

Simplifying
x + -0.6 = -4.284857057

Reorder the terms:
-0.6 + x = -4.284857057

Solving
-0.6 + x = -4.284857057

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -4.284857057 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -4.284857057 + 0.6
x = -4.284857057 + 0.6

Combine like terms: -4.284857057 + 0.6 = -3.684857057
x = -3.684857057

Simplifying
x = -3.684857057


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.884857057, -3.684857057}
Solution
x = {4.884857057, -3.684857057}

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