3x^2-45x=-150

Solution for 3x^2-45x=-150 equation:

Simplifying
3x2 + -45x = -150

Reorder the terms:
-45x + 3x2 = -150

Solving
-45x + 3x2 = -150

Solving for variable 'x'.

Reorder the terms:
150 + -45x + 3x2 = -150 + 150

Combine like terms: -150 + 150 = 0
150 + -45x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(50 + -15x + x2) = 0

Factor a trinomial.
3((5 + -1x)(10 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {5, 10}