6=3x^2+7x

Solution for 6=3x^2+7x equation:

Simplifying
6 = 3x2 + 7x

Reorder the terms:
6 = 7x + 3x2

Solving
6 = 7x + 3x2

Solving for variable 'x'.

Reorder the terms:
6 + -7x + -3x2 = 7x + -7x + 3x2 + -3x2

Combine like terms: 7x + -7x = 0
6 + -7x + -3x2 = 0 + 3x2 + -3x2
6 + -7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -7x + -3x2 = 0

Factor a trinomial.
(2 + -3x)(3 + x) = 0

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
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
Solution
x = {0.6666666667, -3}