10(x-20)(x-20)=1000

Solution for 10(x-20)(x-20)=1000 equation:

Simplifying
10(x + -20)(x + -20) = 1000

Reorder the terms:
10(-20 + x)(x + -20) = 1000

Reorder the terms:
10(-20 + x)(-20 + x) = 1000

Multiply (-20 + x) * (-20 + x)
10(-20(-20 + x) + x(-20 + x)) = 1000
10((-20 * -20 + x * -20) + x(-20 + x)) = 1000
10((400 + -20x) + x(-20 + x)) = 1000
10(400 + -20x + (-20 * x + x * x)) = 1000
10(400 + -20x + (-20x + x2)) = 1000

Combine like terms: -20x + -20x = -40x
10(400 + -40x + x2) = 1000
(400 * 10 + -40x * 10 + x2 * 10) = 1000
(4000 + -400x + 10x2) = 1000

Solving
4000 + -400x + 10x2 = 1000

Solving for variable 'x'.

Reorder the terms:
4000 + -1000 + -400x + 10x2 = 1000 + -1000

Combine like terms: 4000 + -1000 = 3000
3000 + -400x + 10x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
3000 + -400x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(300 + -40x + x2) = 0

Factor a trinomial.
10((10 + -1x)(30 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {10, 30}