4x(x-3)-2=92

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Solution for 4x(x-3)-2=92 equation: 


Simplifying
4x(x + -3) + -2 = 92

Reorder the terms:
4x(-3 + x) + -2 = 92
(-3 * 4x + x * 4x) + -2 = 92
(-12x + 4x2) + -2 = 92

Reorder the terms:
-2 + -12x + 4x2 = 92

Solving
-2 + -12x + 4x2 = 92

Solving for variable 'x'.

Reorder the terms:
-2 + -92 + -12x + 4x2 = 92 + -92

Combine like terms: -2 + -92 = -94
-94 + -12x + 4x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-94 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + -6x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-47 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-47 + -6x + 2x2 = 0

Solving
-47 + -6x + 2x2 = 0

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

Divide each side by '2'.
-23.5 + -3x + x2 = 0

Move the constant term to the right:

Add '23.5' to each side of the equation.
-23.5 + -3x + 23.5 + x2 = 0 + 23.5

Reorder the terms:
-23.5 + 23.5 + -3x + x2 = 0 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + -3x + x2 = 0 + 23.5
-3x + x2 = 0 + 23.5

Combine like terms: 0 + 23.5 = 23.5
-3x + x2 = 23.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 23.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 23.5 + 2.25

Combine like terms: 23.5 + 2.25 = 25.75
2.25 + -3x + x2 = 25.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 25.75

Calculate the square root of the right side: 5.074445783

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.074445783 and -5.074445783.


Subproblem 1
x + -1.5 = 5.074445783

Simplifying
x + -1.5 = 5.074445783

Reorder the terms:
-1.5 + x = 5.074445783

Solving
-1.5 + x = 5.074445783

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 5.074445783 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 5.074445783 + 1.5
x = 5.074445783 + 1.5

Combine like terms: 5.074445783 + 1.5 = 6.574445783
x = 6.574445783

Simplifying
x = 6.574445783


Subproblem 2
x + -1.5 = -5.074445783

Simplifying
x + -1.5 = -5.074445783

Reorder the terms:
-1.5 + x = -5.074445783

Solving
-1.5 + x = -5.074445783

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -5.074445783 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -5.074445783 + 1.5
x = -5.074445783 + 1.5

Combine like terms: -5.074445783 + 1.5 = -3.574445783
x = -3.574445783

Simplifying
x = -3.574445783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.574445783, -3.574445783}
Solution
x = {6.574445783, -3.574445783}

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