4x^2-17x+33=7x+6

Solution for 4x^2-17x+33=7x+6 equation:

Simplifying
4x2 + -17x + 33 = 7x + 6

Reorder the terms:
33 + -17x + 4x2 = 7x + 6

Reorder the terms:
33 + -17x + 4x2 = 6 + 7x

Solving
33 + -17x + 4x2 = 6 + 7x

Solving for variable 'x'.

Reorder the terms:
33 + -6 + -17x + -7x + 4x2 = 6 + 7x + -6 + -7x

Combine like terms: 33 + -6 = 27
27 + -17x + -7x + 4x2 = 6 + 7x + -6 + -7x

Combine like terms: -17x + -7x = -24x
27 + -24x + 4x2 = 6 + 7x + -6 + -7x

Reorder the terms:
27 + -24x + 4x2 = 6 + -6 + 7x + -7x

Combine like terms: 6 + -6 = 0
27 + -24x + 4x2 = 0 + 7x + -7x
27 + -24x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
27 + -24x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(9 + -2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1.5, 4.5}