=6r^2+29r-42

Solution for =6r^2+29r-42 equation:

Simplifying
0 = 6r2 + 29r + -42

Reorder the terms:
0 = -42 + 29r + 6r2

Solving
0 = -42 + 29r + 6r2

Solving for variable 'r'.

Combine like terms: 0 + 42 = 42
42 + -29r + -6r2 = -42 + 29r + 6r2 + 42 + -29r + -6r2

Reorder the terms:
42 + -29r + -6r2 = -42 + 42 + 29r + -29r + 6r2 + -6r2

Combine like terms: -42 + 42 = 0
42 + -29r + -6r2 = 0 + 29r + -29r + 6r2 + -6r2
42 + -29r + -6r2 = 29r + -29r + 6r2 + -6r2

Combine like terms: 29r + -29r = 0
42 + -29r + -6r2 = 0 + 6r2 + -6r2
42 + -29r + -6r2 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
42 + -29r + -6r2 = 0

Factor a trinomial.
(7 + -6r)(6 + r) = 0

Subproblem 1
Set the factor '(7 + -6r)' equal to zero and attempt to solve:

Simplifying
7 + -6r = 0

Solving
7 + -6r = 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 + -6r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6r = 0 + -7
-6r = 0 + -7

Combine like terms: 0 + -7 = -7
-6r = -7

Divide each side by '-6'.
r = 1.166666667

Simplifying
r = 1.166666667
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

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

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {1.166666667, -6}