4x^2-17x+42=8x+6

Solution for 4x^2-17x+42=8x+6 equation:

Simplifying
4x2 + -17x + 42 = 8x + 6

Reorder the terms:
42 + -17x + 4x2 = 8x + 6

Reorder the terms:
42 + -17x + 4x2 = 6 + 8x

Solving
42 + -17x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
42 + -6 + -17x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: 42 + -6 = 36
36 + -17x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -17x + -8x = -25x
36 + -25x + 4x2 = 6 + 8x + -6 + -8x

Reorder the terms:
36 + -25x + 4x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
36 + -25x + 4x2 = 0 + 8x + -8x
36 + -25x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
36 + -25x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.25, 4}