7x(x-1)=42

Solution for 7x(x-1)=42 equation:

Simplifying
7x(x + -1) = 42

Reorder the terms:
7x(-1 + x) = 42
(-1 * 7x + x * 7x) = 42
(-7x + 7x2) = 42

Solving
-7x + 7x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -7x + 7x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -7x + 7x2 = 0

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

Factor a trinomial.
7((-2 + -1x)(3 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}