3x(6x-3)=42

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Solution for 3x(6x-3)=42 equation: 


Simplifying
3x(6x + -3) = 42

Reorder the terms:
3x(-3 + 6x) = 42
(-3 * 3x + 6x * 3x) = 42
(-9x + 18x2) = 42

Solving
-9x + 18x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -9x + 18x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -9x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -3x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-14 + -3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-14 + -3x + 6x2 = 0

Solving
-14 + -3x + 6x2 = 0

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

Divide each side by '6'.
-2.333333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -0.5x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -0.5x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -0.5x + x2 = 0 + 2.333333333
-0.5x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-0.5x + x2 = 2.333333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 2.333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 2.333333333 + 0.0625

Combine like terms: 2.333333333 + 0.0625 = 2.395833333
0.0625 + -0.5x + x2 = 2.395833333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 2.395833333

Calculate the square root of the right side: 1.547847968

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.547847968 and -1.547847968.


Subproblem 1
x + -0.25 = 1.547847968

Simplifying
x + -0.25 = 1.547847968

Reorder the terms:
-0.25 + x = 1.547847968

Solving
-0.25 + x = 1.547847968

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.547847968 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.547847968 + 0.25
x = 1.547847968 + 0.25

Combine like terms: 1.547847968 + 0.25 = 1.797847968
x = 1.797847968

Simplifying
x = 1.797847968


Subproblem 2
x + -0.25 = -1.547847968

Simplifying
x + -0.25 = -1.547847968

Reorder the terms:
-0.25 + x = -1.547847968

Solving
-0.25 + x = -1.547847968

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.547847968 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.547847968 + 0.25
x = -1.547847968 + 0.25

Combine like terms: -1.547847968 + 0.25 = -1.297847968
x = -1.297847968

Simplifying
x = -1.297847968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.797847968, -1.297847968}
Solution
x = {1.797847968, -1.297847968}

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