2x^2+28x+41=-7

Solution for 2x^2+28x+41=-7 equation:

Simplifying
2x2 + 28x + 41 = -7

Reorder the terms:
41 + 28x + 2x2 = -7

Solving
41 + 28x + 2x2 = -7

Solving for variable 'x'.

Reorder the terms:
41 + 7 + 28x + 2x2 = -7 + 7

Combine like terms: 41 + 7 = 48
48 + 28x + 2x2 = -7 + 7

Combine like terms: -7 + 7 = 0
48 + 28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 14x + x2) = 0

Factor a trinomial.
2((12 + x)(2 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-12, -2}