5x^2=x+42

Solution for 5x^2=x+42 equation:

Simplifying
5x2 = x + 42

Reorder the terms:
5x2 = 42 + x

Solving
5x2 = 42 + x

Solving for variable 'x'.

Reorder the terms:
-42 + -1x + 5x2 = 42 + x + -42 + -1x

Reorder the terms:
-42 + -1x + 5x2 = 42 + -42 + x + -1x

Combine like terms: 42 + -42 = 0
-42 + -1x + 5x2 = 0 + x + -1x
-42 + -1x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-42 + -1x + 5x2 = 0

Factor a trinomial.
(-14 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -5x)' equal to zero and attempt to solve:

Simplifying
-14 + -5x = 0

Solving
-14 + -5x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -5x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -5x = 0 + 14
-5x = 0 + 14

Combine like terms: 0 + 14 = 14
-5x = 14

Divide each side by '-5'.
x = -2.8

Simplifying
x = -2.8
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 = {-2.8, 3}