1050=x(100-2x)

Solution for 1050=x(100-2x) equation:

Simplifying
1050 = x(100 + -2x)
1050 = (100 * x + -2x * x)
1050 = (100x + -2x2)

Solving
1050 = 100x + -2x2

Solving for variable 'x'.

Reorder the terms:
1050 + -100x + 2x2 = 100x + -100x + -2x2 + 2x2

Combine like terms: 100x + -100x = 0
1050 + -100x + 2x2 = 0 + -2x2 + 2x2
1050 + -100x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
1050 + -100x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(525 + -50x + x2) = 0

Factor a trinomial.
2((15 + -1x)(35 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Solution
x = {15, 35}