30x-75=3x^2

Solution for 30x-75=3x^2 equation:

Simplifying
30x + -75 = 3x2

Reorder the terms:
-75 + 30x = 3x2

Solving
-75 + 30x = 3x2

Solving for variable 'x'.

Combine like terms: 3x2 + -3x2 = 0
-75 + 30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 10x + -1x2) = 0

Factor a trinomial.
3((-5 + x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {5, 5}