4r^2+2r-42=0

Solution for 4r^2+2r-42=0 equation:

Simplifying
4r2 + 2r + -42 = 0

Reorder the terms:
-42 + 2r + 4r2 = 0

Solving
-42 + 2r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + r + 2r2) = 0

Factor a trinomial.
2((-7 + -2r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -2r)' equal to zero and attempt to solve:

Simplifying
-7 + -2r = 0

Solving
-7 + -2r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2r = 0 + 7
-2r = 0 + 7

Combine like terms: 0 + 7 = 7
-2r = 7

Divide each side by '-2'.
r = -3.5

Simplifying
r = -3.5
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-3.5, 3}