100x(x-3)=450-50

Solution for 100x(x-3)=450-50 equation:

Simplifying
100x(x + -3) = 450 + -50

Reorder the terms:
100x(-3 + x) = 450 + -50
(-3 * 100x + x * 100x) = 450 + -50
(-300x + 100x2) = 450 + -50

Combine like terms: 450 + -50 = 400
-300x + 100x2 = 400

Solving
-300x + 100x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -300x + 100x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -300x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-4 + -3x + x2) = 0

Factor a trinomial.
100((-1 + -1x)(4 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}