40r^2-318r-144=-2r^2

Solution for 40r^2-318r-144=-2r^2 equation:

Simplifying
40r2 + -318r + -144 = -2r2

Reorder the terms:
-144 + -318r + 40r2 = -2r2

Solving
-144 + -318r + 40r2 = -2r2

Solving for variable 'r'.

Combine like terms: 40r2 + 2r2 = 42r2
-144 + -318r + 42r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
-144 + -318r + 42r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-24 + -53r + 7r2) = 0

Factor a trinomial.
6((-3 + -7r)(8 + -1r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -7r)' equal to zero and attempt to solve:

Simplifying
-3 + -7r = 0

Solving
-3 + -7r = 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 + -7r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7r = 0 + 3
-7r = 0 + 3

Combine like terms: 0 + 3 = 3
-7r = 3

Divide each side by '-7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-0.4285714286, 8}