4x^2-27x+51=2x+6

Solution for 4x^2-27x+51=2x+6 equation:

Simplifying
4x2 + -27x + 51 = 2x + 6

Reorder the terms:
51 + -27x + 4x2 = 2x + 6

Reorder the terms:
51 + -27x + 4x2 = 6 + 2x

Solving
51 + -27x + 4x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
51 + -6 + -27x + -2x + 4x2 = 6 + 2x + -6 + -2x

Combine like terms: 51 + -6 = 45
45 + -27x + -2x + 4x2 = 6 + 2x + -6 + -2x

Combine like terms: -27x + -2x = -29x
45 + -29x + 4x2 = 6 + 2x + -6 + -2x

Reorder the terms:
45 + -29x + 4x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
45 + -29x + 4x2 = 0 + 2x + -2x
45 + -29x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
45 + -29x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(5 + -1x) = 0

Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2.25, 5}