30x-45=5x^2

Solution for 30x-45=5x^2 equation:

Simplifying
30x + -45 = 5x2

Reorder the terms:
-45 + 30x = 5x2

Solving
-45 + 30x = 5x2

Solving for variable 'x'.

Combine like terms: 5x2 + -5x2 = 0
-45 + 30x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 6x + -1x2) = 0

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

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}