4x^2-17x+27=2x+6

Solution for 4x^2-17x+27=2x+6 equation:

Simplifying
4x2 + -17x + 27 = 2x + 6

Reorder the terms:
27 + -17x + 4x2 = 2x + 6

Reorder the terms:
27 + -17x + 4x2 = 6 + 2x

Solving
27 + -17x + 4x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
27 + -6 + -17x + -2x + 4x2 = 6 + 2x + -6 + -2x

Combine like terms: 27 + -6 = 21
21 + -17x + -2x + 4x2 = 6 + 2x + -6 + -2x

Combine like terms: -17x + -2x = -19x
21 + -19x + 4x2 = 6 + 2x + -6 + -2x

Reorder the terms:
21 + -19x + 4x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
21 + -19x + 4x2 = 0 + 2x + -2x
21 + -19x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
21 + -19x + 4x2 = 0

Factor a trinomial.
(7 + -4x)(3 + -1x) = 0

Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.75, 3}