-3X^2+6=7X

Solution for -3X^2+6=7X equation:

Simplifying
-3X2 + 6 = 7X

Reorder the terms:
6 + -3X2 = 7X

Solving
6 + -3X2 = 7X

Solving for variable 'X'.

Reorder the terms:
6 + -7X + -3X2 = 7X + -7X

Combine like terms: 7X + -7X = 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}