x(2x-100)=30000

Solution for x(2x-100)=30000 equation:

Simplifying
x(2x + -100) = 30000

Reorder the terms:
x(-100 + 2x) = 30000
(-100 * x + 2x * x) = 30000
(-100x + 2x2) = 30000

Solving
-100x + 2x2 = 30000

Solving for variable 'x'.

Reorder the terms:
-30000 + -100x + 2x2 = 30000 + -30000

Combine like terms: 30000 + -30000 = 0
-30000 + -100x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15000 + -50x + x2) = 0

Factor a trinomial.
2((-100 + -1x)(150 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-100 + -1x)' equal to zero and attempt to solve:

Simplifying
-100 + -1x = 0

Solving
-100 + -1x = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1x = 0 + 100
-1x = 0 + 100

Combine like terms: 0 + 100 = 100
-1x = 100

Divide each side by '-1'.
x = -100

Simplifying
x = -100
Subproblem 2
Set the factor '(150 + -1x)' equal to zero and attempt to solve:

Simplifying
150 + -1x = 0

Solving
150 + -1x = 0

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

Add '-150' to each side of the equation.
150 + -150 + -1x = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -1x = 0 + -150
-1x = 0 + -150

Combine like terms: 0 + -150 = -150
-1x = -150

Divide each side by '-1'.
x = 150

Simplifying
x = 150
Solution
x = {-100, 150}