12x^2+9x=8x+6

Solution for 12x^2+9x=8x+6 equation:

Simplifying
12x2 + 9x = 8x + 6

Reorder the terms:
9x + 12x2 = 8x + 6

Reorder the terms:
9x + 12x2 = 6 + 8x

Solving
9x + 12x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
-6 + 9x + -8x + 12x2 = 6 + 8x + -6 + -8x

Combine like terms: 9x + -8x = 1x
-6 + 1x + 12x2 = 6 + 8x + -6 + -8x

Reorder the terms:
-6 + 1x + 12x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
-6 + 1x + 12x2 = 0 + 8x + -8x
-6 + 1x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-6 + 1x + 12x2 = 0

Factor a trinomial.
(-3 + -4x)(2 + -3x) = 0

Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, 0.6666666667}