(2r+3)(r-8)=-(5r-40)

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Solution for (2r+3)(r-8)=-(5r-40) equation:


Simplifying
(2r + 3)(r + -8) = -1(5r + -40)

Reorder the terms:
(3 + 2r)(r + -8) = -1(5r + -40)

Reorder the terms:
(3 + 2r)(-8 + r) = -1(5r + -40)

Multiply (3 + 2r) * (-8 + r)
(3(-8 + r) + 2r * (-8 + r)) = -1(5r + -40)
((-8 * 3 + r * 3) + 2r * (-8 + r)) = -1(5r + -40)
((-24 + 3r) + 2r * (-8 + r)) = -1(5r + -40)
(-24 + 3r + (-8 * 2r + r * 2r)) = -1(5r + -40)
(-24 + 3r + (-16r + 2r2)) = -1(5r + -40)

Combine like terms: 3r + -16r = -13r
(-24 + -13r + 2r2) = -1(5r + -40)

Reorder the terms:
-24 + -13r + 2r2 = -1(-40 + 5r)
-24 + -13r + 2r2 = (-40 * -1 + 5r * -1)
-24 + -13r + 2r2 = (40 + -5r)

Solving
-24 + -13r + 2r2 = 40 + -5r

Solving for variable 'r'.

Reorder the terms:
-24 + -40 + -13r + 5r + 2r2 = 40 + -5r + -40 + 5r

Combine like terms: -24 + -40 = -64
-64 + -13r + 5r + 2r2 = 40 + -5r + -40 + 5r

Combine like terms: -13r + 5r = -8r
-64 + -8r + 2r2 = 40 + -5r + -40 + 5r

Reorder the terms:
-64 + -8r + 2r2 = 40 + -40 + -5r + 5r

Combine like terms: 40 + -40 = 0
-64 + -8r + 2r2 = 0 + -5r + 5r
-64 + -8r + 2r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
-64 + -8r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -4r + r2) = 0

Factor a trinomial.
2((-4 + -1r)(8 + -1r)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4

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 = {-4, 8}

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