100*(x*x)+900x=414000

Solution for 100*(x*x)+900x=414000 equation:

Simplifying
100(x * x) + 900x = 414000

Multiply x * x
100(x2) + 900x = 414000

Reorder the terms:
900x + 100x2 = 414000

Solving
900x + 100x2 = 414000

Solving for variable 'x'.

Reorder the terms:
-414000 + 900x + 100x2 = 414000 + -414000

Combine like terms: 414000 + -414000 = 0
-414000 + 900x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-4140 + 9x + x2) = 0

Factor a trinomial.
100((-69 + -1x)(60 + -1x)) = 0

Ignore the factor 100.
Subproblem 1
Set the factor '(-69 + -1x)' equal to zero and attempt to solve:

Simplifying
-69 + -1x = 0

Solving
-69 + -1x = 0

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

Add '69' to each side of the equation.
-69 + 69 + -1x = 0 + 69

Combine like terms: -69 + 69 = 0
0 + -1x = 0 + 69
-1x = 0 + 69

Combine like terms: 0 + 69 = 69
-1x = 69

Divide each side by '-1'.
x = -69

Simplifying
x = -69
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {-69, 60}