430x-(x^2+20x+4000)=0

Solution for 430x-(x^2+20x+4000)=0 equation:

Simplifying
430x + -1(x2 + 20x + 4000) = 0

Reorder the terms:
430x + -1(4000 + 20x + x2) = 0
430x + (4000 * -1 + 20x * -1 + x2 * -1) = 0
430x + (-4000 + -20x + -1x2) = 0

Reorder the terms:
-4000 + 430x + -20x + -1x2 = 0

Combine like terms: 430x + -20x = 410x
-4000 + 410x + -1x2 = 0

Solving
-4000 + 410x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-400 + x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-400 + x)' equal to zero and attempt to solve:

Simplifying
-400 + x = 0

Solving
-400 + x = 0

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

Add '400' to each side of the equation.
-400 + 400 + x = 0 + 400

Combine like terms: -400 + 400 = 0
0 + x = 0 + 400
x = 0 + 400

Combine like terms: 0 + 400 = 400
x = 400

Simplifying
x = 400
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {400, 10}