(r+2)(r-5)(r-2)(r+5)=

Solution for (r+2)(r-5)(r-2)(r+5)= equation:

Simplifying
(r + 2)(r + -5)(r + -2)(r + 5) = 0

Reorder the terms:
(2 + r)(r + -5)(r + -2)(r + 5) = 0

Reorder the terms:
(2 + r)(-5 + r)(r + -2)(r + 5) = 0

Reorder the terms:
(2 + r)(-5 + r)(-2 + r)(r + 5) = 0

Reorder the terms:
(2 + r)(-5 + r)(-2 + r)(5 + r) = 0

Multiply (2 + r) * (-5 + r)
(2(-5 + r) + r(-5 + r))(-2 + r)(5 + r) = 0
((-5 * 2 + r * 2) + r(-5 + r))(-2 + r)(5 + r) = 0
((-10 + 2r) + r(-5 + r))(-2 + r)(5 + r) = 0
(-10 + 2r + (-5 * r + r * r))(-2 + r)(5 + r) = 0
(-10 + 2r + (-5r + r2))(-2 + r)(5 + r) = 0

Combine like terms: 2r + -5r = -3r
(-10 + -3r + r2)(-2 + r)(5 + r) = 0

Multiply (-10 + -3r + r2) * (-2 + r)
(-10(-2 + r) + -3r * (-2 + r) + r2(-2 + r))(5 + r) = 0
((-2 * -10 + r * -10) + -3r * (-2 + r) + r2(-2 + r))(5 + r) = 0
((20 + -10r) + -3r * (-2 + r) + r2(-2 + r))(5 + r) = 0
(20 + -10r + (-2 * -3r + r * -3r) + r2(-2 + r))(5 + r) = 0
(20 + -10r + (6r + -3r2) + r2(-2 + r))(5 + r) = 0
(20 + -10r + 6r + -3r2 + (-2 * r2 + r * r2))(5 + r) = 0
(20 + -10r + 6r + -3r2 + (-2r2 + r3))(5 + r) = 0

Combine like terms: -10r + 6r = -4r
(20 + -4r + -3r2 + -2r2 + r3)(5 + r) = 0

Combine like terms: -3r2 + -2r2 = -5r2
(20 + -4r + -5r2 + r3)(5 + r) = 0

Multiply (20 + -4r + -5r2 + r3) * (5 + r)
(20(5 + r) + -4r * (5 + r) + -5r2 * (5 + r) + r3(5 + r)) = 0
((5 * 20 + r * 20) + -4r * (5 + r) + -5r2 * (5 + r) + r3(5 + r)) = 0
((100 + 20r) + -4r * (5 + r) + -5r2 * (5 + r) + r3(5 + r)) = 0
(100 + 20r + (5 * -4r + r * -4r) + -5r2 * (5 + r) + r3(5 + r)) = 0
(100 + 20r + (-20r + -4r2) + -5r2 * (5 + r) + r3(5 + r)) = 0
(100 + 20r + -20r + -4r2 + (5 * -5r2 + r * -5r2) + r3(5 + r)) = 0
(100 + 20r + -20r + -4r2 + (-25r2 + -5r3) + r3(5 + r)) = 0
(100 + 20r + -20r + -4r2 + -25r2 + -5r3 + (5 * r3 + r * r3)) = 0
(100 + 20r + -20r + -4r2 + -25r2 + -5r3 + (5r3 + r4)) = 0

Combine like terms: 20r + -20r = 0
(100 + 0 + -4r2 + -25r2 + -5r3 + 5r3 + r4) = 0
(100 + -4r2 + -25r2 + -5r3 + 5r3 + r4) = 0

Combine like terms: -4r2 + -25r2 = -29r2
(100 + -29r2 + -5r3 + 5r3 + r4) = 0

Combine like terms: -5r3 + 5r3 = 0
(100 + -29r2 + 0 + r4) = 0
(100 + -29r2 + r4) = 0

Solving
100 + -29r2 + r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + -1r2)(25 + -1r2) = 0

Factor a difference between two squares.
((2 + r)(2 + -1r))(25 + -1r2) = 0

Factor a difference between two squares.
((5 + r)(5 + -1r))(2 + r)(2 + -1r) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Subproblem 3
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

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

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

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

Simplifying
r = -5
Subproblem 4
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-2, 2, -5, 5}