7r^2(3r^2-2r-5)=

Solution for 7r^2(3r^2-2r-5)= equation:

Simplifying
7r2(3r2 + -2r + -5) = 0

Reorder the terms:
7r2(-5 + -2r + 3r2) = 0
(-5 * 7r2 + -2r * 7r2 + 3r2 * 7r2) = 0
(-35r2 + -14r3 + 21r4) = 0

Solving
-35r2 + -14r3 + 21r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7r2'.
7r2(-5 + -2r + 3r2) = 0

Factor a trinomial.
7r2((-1 + -1r)(5 + -3r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(-1 + -1r)' equal to zero and attempt to solve:

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
Subproblem 3
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3r = 0 + -5
-3r = 0 + -5

Combine like terms: 0 + -5 = -5
-3r = -5

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {0, -1, 1.666666667}