4x^2=17x+42

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

Simplifying
4x2 = 17x + 42

Reorder the terms:
4x2 = 42 + 17x

Solving
4x2 = 42 + 17x

Solving for variable 'x'.

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

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

Combine like terms: 42 + -42 = 0
-42 + -17x + 4x2 = 0 + 17x + -17x
-42 + -17x + 4x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-42 + -17x + 4x2 = 0

Factor a trinomial.
(-7 + -4x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1.75, 6}