10x^2+22x+12=0

Solution for 10x^2+22x+12=0 equation:

Simplifying
10x2 + 22x + 12 = 0

Reorder the terms:
12 + 22x + 10x2 = 0

Solving
12 + 22x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 11x + 5x2) = 0

Factor a trinomial.
2((6 + 5x)(1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-1.2, -1}