4x^2+28x+42=-6

Solution for 4x^2+28x+42=-6 equation:

Simplifying
4x2 + 28x + 42 = -6

Reorder the terms:
42 + 28x + 4x2 = -6

Solving
42 + 28x + 4x2 = -6

Solving for variable 'x'.

Reorder the terms:
42 + 6 + 28x + 4x2 = -6 + 6

Combine like terms: 42 + 6 = 48
48 + 28x + 4x2 = -6 + 6

Combine like terms: -6 + 6 = 0
48 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 7x + x2) = 0

Factor a trinomial.
4((4 + x)(3 + x)) = 0

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}