-6r^2-50r+36=(-5r+9)(r+9)

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Solution for -6r^2-50r+36=(-5r+9)(r+9) equation: 


Simplifying
-6r2 + -50r + 36 = (-5r + 9)(r + 9)

Reorder the terms:
36 + -50r + -6r2 = (-5r + 9)(r + 9)

Reorder the terms:
36 + -50r + -6r2 = (9 + -5r)(r + 9)

Reorder the terms:
36 + -50r + -6r2 = (9 + -5r)(9 + r)

Multiply (9 + -5r) * (9 + r)
36 + -50r + -6r2 = (9(9 + r) + -5r * (9 + r))
36 + -50r + -6r2 = ((9 * 9 + r * 9) + -5r * (9 + r))
36 + -50r + -6r2 = ((81 + 9r) + -5r * (9 + r))
36 + -50r + -6r2 = (81 + 9r + (9 * -5r + r * -5r))
36 + -50r + -6r2 = (81 + 9r + (-45r + -5r2))

Combine like terms: 9r + -45r = -36r
36 + -50r + -6r2 = (81 + -36r + -5r2)

Solving
36 + -50r + -6r2 = 81 + -36r + -5r2

Solving for variable 'r'.

Reorder the terms:
36 + -81 + -50r + 36r + -6r2 + 5r2 = 81 + -36r + -5r2 + -81 + 36r + 5r2

Combine like terms: 36 + -81 = -45
-45 + -50r + 36r + -6r2 + 5r2 = 81 + -36r + -5r2 + -81 + 36r + 5r2

Combine like terms: -50r + 36r = -14r
-45 + -14r + -6r2 + 5r2 = 81 + -36r + -5r2 + -81 + 36r + 5r2

Combine like terms: -6r2 + 5r2 = -1r2
-45 + -14r + -1r2 = 81 + -36r + -5r2 + -81 + 36r + 5r2

Reorder the terms:
-45 + -14r + -1r2 = 81 + -81 + -36r + 36r + -5r2 + 5r2

Combine like terms: 81 + -81 = 0
-45 + -14r + -1r2 = 0 + -36r + 36r + -5r2 + 5r2
-45 + -14r + -1r2 = -36r + 36r + -5r2 + 5r2

Combine like terms: -36r + 36r = 0
-45 + -14r + -1r2 = 0 + -5r2 + 5r2
-45 + -14r + -1r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
-45 + -14r + -1r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 14r + r2) = 0

Factor a trinomial.
-1((9 + r)(5 + r)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + r)' equal to zero and attempt to solve:

Simplifying
9 + r = 0

Solving
9 + r = 0

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

Add '-9' to each side of the equation.
9 + -9 + r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + r = 0 + -9
r = 0 + -9

Combine like terms: 0 + -9 = -9
r = -9

Simplifying
r = -9

Subproblem 2
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
Solution
r = {-9, -5}

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