3x^2+6x+3=75

Solution for 3x^2+6x+3=75 equation:

Simplifying
3x2 + 6x + 3 = 75

Reorder the terms:
3 + 6x + 3x2 = 75

Solving
3 + 6x + 3x2 = 75

Solving for variable 'x'.

Reorder the terms:
3 + -75 + 6x + 3x2 = 75 + -75

Combine like terms: 3 + -75 = -72
-72 + 6x + 3x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-72 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 2x + x2) = 0

Factor a trinomial.
3((-6 + -1x)(4 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6, 4}