-6x(x-2)=42

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Solution for -6x(x-2)=42 equation: 


Simplifying
-6x(x + -2) = 42

Reorder the terms:
-6x(-2 + x) = 42
(-2 * -6x + x * -6x) = 42
(12x + -6x2) = 42

Solving
12x + -6x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 12x + -6x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + 2x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
-7 + 2x + -1x2 = 0

Solving
-7 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
7 + -2x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -2x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -2x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x + x2 = 0 + -7
-2x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-2x + x2 = -7

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -7 + 1

Reorder the terms:
1 + -2x + x2 = -7 + 1

Combine like terms: -7 + 1 = -6
1 + -2x + x2 = -6

Factor a perfect square on the left side:
(x + -1)(x + -1) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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