2X^2+2X+6=30

Solution for 2X^2+2X+6=30 equation:

Simplifying
2X2 + 2X + 6 = 30

Reorder the terms:
6 + 2X + 2X2 = 30

Solving
6 + 2X + 2X2 = 30

Solving for variable 'X'.

Reorder the terms:
6 + -30 + 2X + 2X2 = 30 + -30

Combine like terms: 6 + -30 = -24
-24 + 2X + 2X2 = 30 + -30

Combine like terms: 30 + -30 = 0
-24 + 2X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + X + X2) = 0

Factor a trinomial.
2((-4 + -1X)(3 + -1X)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1X)' equal to zero and attempt to solve:

Simplifying
-4 + -1X = 0

Solving
-4 + -1X = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1X = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1X = 0 + 4
-1X = 0 + 4

Combine like terms: 0 + 4 = 4
-1X = 4

Divide each side by '-1'.
X = -4

Simplifying
X = -4
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 = {-4, 3}