=6x^2-78x+252

Solution for =6x^2-78x+252 equation:

Simplifying
0 = 6x2 + -78x + 252

Reorder the terms:
0 = 252 + -78x + 6x2

Solving
0 = 252 + -78x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -252 = -252
-252 + 78x + -6x2 = 252 + -78x + 6x2 + -252 + 78x + -6x2

Reorder the terms:
-252 + 78x + -6x2 = 252 + -252 + -78x + 78x + 6x2 + -6x2

Combine like terms: 252 + -252 = 0
-252 + 78x + -6x2 = 0 + -78x + 78x + 6x2 + -6x2
-252 + 78x + -6x2 = -78x + 78x + 6x2 + -6x2

Combine like terms: -78x + 78x = 0
-252 + 78x + -6x2 = 0 + 6x2 + -6x2
-252 + 78x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-252 + 78x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-42 + 13x + -1x2) = 0

Factor a trinomial.
6((-7 + x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {7, 6}