75x^2-9=-30x

Solution for 75x^2-9=-30x equation:

Simplifying
75x2 + -9 = -30x

Reorder the terms:
-9 + 75x2 = -30x

Solving
-9 + 75x2 = -30x

Solving for variable 'x'.

Reorder the terms:
-9 + 30x + 75x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-9 + 30x + 75x2 = 0

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

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

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

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6
Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

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

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-0.6, 0.2}