100x^2+200x+100=0

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

Simplifying
100x2 + 200x + 100 = 0

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

Solving
100 + 200x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '100'.
100(1 + 2x + x2) = 0

Factor a trinomial.
100((1 + x)(1 + x)) = 0

Ignore the factor 100.
Subproblem 1
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
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, -1}