0=6x^2-48x+42

Solution for 0=6x^2-48x+42 equation:

Simplifying
0 = 6x2 + -48x + 42

Reorder the terms:
0 = 42 + -48x + 6x2

Solving
0 = 42 + -48x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + 48x + -6x2 = 42 + -48x + 6x2 + -42 + 48x + -6x2

Reorder the terms:
-42 + 48x + -6x2 = 42 + -42 + -48x + 48x + 6x2 + -6x2

Combine like terms: 42 + -42 = 0
-42 + 48x + -6x2 = 0 + -48x + 48x + 6x2 + -6x2
-42 + 48x + -6x2 = -48x + 48x + 6x2 + -6x2

Combine like terms: -48x + 48x = 0
-42 + 48x + -6x2 = 0 + 6x2 + -6x2
-42 + 48x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-42 + 48x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + 8x + -1x2) = 0

Factor a trinomial.
6((-7 + x)(1 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

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

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

Combine like terms: 0 + 7 = 7
x = 7

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {7, 1}