-3x^2+270x-4200=1875

Solution for -3x^2+270x-4200=1875 equation:

Simplifying
-3x2 + 270x + -4200 = 1875

Reorder the terms:
-4200 + 270x + -3x2 = 1875

Solving
-4200 + 270x + -3x2 = 1875

Solving for variable 'x'.

Reorder the terms:
-4200 + -1875 + 270x + -3x2 = 1875 + -1875

Combine like terms: -4200 + -1875 = -6075
-6075 + 270x + -3x2 = 1875 + -1875

Combine like terms: 1875 + -1875 = 0
-6075 + 270x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2025 + 90x + -1x2) = 0

Factor a trinomial.
3((-45 + x)(45 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-45 + x)' equal to zero and attempt to solve:

Simplifying
-45 + x = 0

Solving
-45 + x = 0

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

Add '45' to each side of the equation.
-45 + 45 + x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + x = 0 + 45
x = 0 + 45

Combine like terms: 0 + 45 = 45
x = 45

Simplifying
x = 45
Subproblem 2
Set the factor '(45 + -1x)' equal to zero and attempt to solve:

Simplifying
45 + -1x = 0

Solving
45 + -1x = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1x = 0 + -45
-1x = 0 + -45

Combine like terms: 0 + -45 = -45
-1x = -45

Divide each side by '-1'.
x = 45

Simplifying
x = 45
Solution
x = {45, 45}