4200=-3(x^2-90x)

Solution for 4200=-3(x^2-90x) equation:

Simplifying
4200 = -3(x2 + -90x)

Reorder the terms:
4200 = -3(-90x + x2)
4200 = (-90x * -3 + x2 * -3)
4200 = (270x + -3x2)

Solving
4200 = 270x + -3x2

Solving for variable 'x'.

Reorder the terms:
4200 + -270x + 3x2 = 270x + -270x + -3x2 + 3x2

Combine like terms: 270x + -270x = 0
4200 + -270x + 3x2 = 0 + -3x2 + 3x2
4200 + -270x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
4200 + -270x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1400 + -90x + x2) = 0

Factor a trinomial.
3((20 + -1x)(70 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve:

Simplifying
70 + -1x = 0

Solving
70 + -1x = 0

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

Add '-70' to each side of the equation.
70 + -70 + -1x = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -1x = 0 + -70
-1x = 0 + -70

Combine like terms: 0 + -70 = -70
-1x = -70

Divide each side by '-1'.
x = 70

Simplifying
x = 70
Solution
x = {20, 70}