4x^2-3x+11=9x+6

Solution for 4x^2-3x+11=9x+6 equation:

Simplifying
4x2 + -3x + 11 = 9x + 6

Reorder the terms:
11 + -3x + 4x2 = 9x + 6

Reorder the terms:
11 + -3x + 4x2 = 6 + 9x

Solving
11 + -3x + 4x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
11 + -6 + -3x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: 11 + -6 = 5
5 + -3x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: -3x + -9x = -12x
5 + -12x + 4x2 = 6 + 9x + -6 + -9x

Reorder the terms:
5 + -12x + 4x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
5 + -12x + 4x2 = 0 + 9x + -9x
5 + -12x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
5 + -12x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(5 + -2x) = 0

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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.5, 2.5}