200x^2+100x+12=0

Solution for 200x^2+100x+12=0 equation:

Simplifying
200x2 + 100x + 12 = 0

Reorder the terms:
12 + 100x + 200x2 = 0

Solving
12 + 100x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 25x + 50x2) = 0

Factor a trinomial.
4((3 + 10x)(1 + 5x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 10x)' equal to zero and attempt to solve:

Simplifying
3 + 10x = 0

Solving
3 + 10x = 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 + 10x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 10x = 0 + -3
10x = 0 + -3

Combine like terms: 0 + -3 = -3
10x = -3

Divide each side by '10'.
x = -0.3

Simplifying
x = -0.3
Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-0.3, -0.2}