x+5x^2-42=0

Solution for x+5x^2-42=0 equation:

Simplifying
x + 5x2 + -42 = 0

Reorder the terms:
-42 + x + 5x2 = 0

Solving
-42 + x + 5x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 2.8}