6x^2+4x=9x+6

Solution for 6x^2+4x=9x+6 equation:

Simplifying
6x2 + 4x = 9x + 6

Reorder the terms:
4x + 6x2 = 9x + 6

Reorder the terms:
4x + 6x2 = 6 + 9x

Solving
4x + 6x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
-6 + 4x + -9x + 6x2 = 6 + 9x + -6 + -9x

Combine like terms: 4x + -9x = -5x
-6 + -5x + 6x2 = 6 + 9x + -6 + -9x

Reorder the terms:
-6 + -5x + 6x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
-6 + -5x + 6x2 = 0 + 9x + -9x
-6 + -5x + 6x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-6 + -5x + 6x2 = 0

Factor a trinomial.
(-2 + -3x)(3 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.6666666667, 1.5}