10r^2=23r+42

Solution for 10r^2=23r+42 equation:

Simplifying
10r2 = 23r + 42

Reorder the terms:
10r2 = 42 + 23r

Solving
10r2 = 42 + 23r

Solving for variable 'r'.

Reorder the terms:
-42 + -23r + 10r2 = 42 + 23r + -42 + -23r

Reorder the terms:
-42 + -23r + 10r2 = 42 + -42 + 23r + -23r

Combine like terms: 42 + -42 = 0
-42 + -23r + 10r2 = 0 + 23r + -23r
-42 + -23r + 10r2 = 23r + -23r

Combine like terms: 23r + -23r = 0
-42 + -23r + 10r2 = 0

Factor a trinomial.
(-6 + -5r)(7 + -2r) = 0

Subproblem 1
Set the factor '(-6 + -5r)' equal to zero and attempt to solve:

Simplifying
-6 + -5r = 0

Solving
-6 + -5r = 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 + -5r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5r = 0 + 6
-5r = 0 + 6

Combine like terms: 0 + 6 = 6
-5r = 6

Divide each side by '-5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
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
Solution
r = {-1.2, 3.5}