2x^2-14x-54=6

Solution for 2x^2-14x-54=6 equation:

Simplifying
2x2 + -14x + -54 = 6

Reorder the terms:
-54 + -14x + 2x2 = 6

Solving
-54 + -14x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-54 + -6 + -14x + 2x2 = 6 + -6

Combine like terms: -54 + -6 = -60
-60 + -14x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-60 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -7x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-3, 10}