2x^2+13x+27=6

Solution for 2x^2+13x+27=6 equation:

Simplifying
2x2 + 13x + 27 = 6

Reorder the terms:
27 + 13x + 2x2 = 6

Solving
27 + 13x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
27 + -6 + 13x + 2x2 = 6 + -6

Combine like terms: 27 + -6 = 21
21 + 13x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
21 + 13x + 2x2 = 0

Factor a trinomial.
(7 + 2x)(3 + x) = 0

Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
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 = {-3.5, -3}