3x^2+4x=x+6

Solution for 3x^2+4x=x+6 equation:

Simplifying
3x2 + 4x = x + 6

Reorder the terms:
4x + 3x2 = x + 6

Reorder the terms:
4x + 3x2 = 6 + x

Solving
4x + 3x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-6 + 4x + -1x + 3x2 = 6 + x + -6 + -1x

Combine like terms: 4x + -1x = 3x
-6 + 3x + 3x2 = 6 + x + -6 + -1x

Reorder the terms:
-6 + 3x + 3x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
-6 + 3x + 3x2 = 0 + x + -1x
-6 + 3x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + 3x + 3x2 = 0

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

Factor a trinomial.
3((-2 + -1x)(1 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-2, 1}