3x(2x-10)=180

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Solution for 3x(2x-10)=180 equation: 


Simplifying
3x(2x + -10) = 180

Reorder the terms:
3x(-10 + 2x) = 180
(-10 * 3x + 2x * 3x) = 180
(-30x + 6x2) = 180

Solving
-30x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -30x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + -5x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + -5x + x2 = 0

Solving
-30 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -5x + x2 = 0 + 30
-5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-5x + x2 = 30

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 30 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 30 + 6.25

Combine like terms: 30 + 6.25 = 36.25
6.25 + -5x + x2 = 36.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + -2.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + -2.5 = 6.020797289

Simplifying
x + -2.5 = 6.020797289

Reorder the terms:
-2.5 + x = 6.020797289

Solving
-2.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 6.020797289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 6.020797289 + 2.5
x = 6.020797289 + 2.5

Combine like terms: 6.020797289 + 2.5 = 8.520797289
x = 8.520797289

Simplifying
x = 8.520797289


Subproblem 2
x + -2.5 = -6.020797289

Simplifying
x + -2.5 = -6.020797289

Reorder the terms:
-2.5 + x = -6.020797289

Solving
-2.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -6.020797289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -6.020797289 + 2.5
x = -6.020797289 + 2.5

Combine like terms: -6.020797289 + 2.5 = -3.520797289
x = -3.520797289

Simplifying
x = -3.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.520797289, -3.520797289}
Solution
x = {8.520797289, -3.520797289}

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