(-6X^2)+(60X)-126=0

Solution for (-6X^2)+(60X)-126=0 equation:

Simplifying
(-6X2) + (60X) + -126 = 0

Reorder the terms:
-126 + (60X) + (-6X2) = 0

Solving
-126 + (60X) + (-6X2) = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + (10X) + (-1X2)) = 0

Factor a trinomial.
6((-7 + X)(3 + -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 '(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 = {7, 3}