(4r+3)(r-8)=-(5r-40)

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Solution for (4r+3)(r-8)=-(5r-40) equation: 


Simplifying
(4r + 3)(r + -8) = -1(5r + -40)

Reorder the terms:
(3 + 4r)(r + -8) = -1(5r + -40)

Reorder the terms:
(3 + 4r)(-8 + r) = -1(5r + -40)

Multiply (3 + 4r) * (-8 + r)
(3(-8 + r) + 4r * (-8 + r)) = -1(5r + -40)
((-8 * 3 + r * 3) + 4r * (-8 + r)) = -1(5r + -40)
((-24 + 3r) + 4r * (-8 + r)) = -1(5r + -40)
(-24 + 3r + (-8 * 4r + r * 4r)) = -1(5r + -40)
(-24 + 3r + (-32r + 4r2)) = -1(5r + -40)

Combine like terms: 3r + -32r = -29r
(-24 + -29r + 4r2) = -1(5r + -40)

Reorder the terms:
-24 + -29r + 4r2 = -1(-40 + 5r)
-24 + -29r + 4r2 = (-40 * -1 + 5r * -1)
-24 + -29r + 4r2 = (40 + -5r)

Solving
-24 + -29r + 4r2 = 40 + -5r

Solving for variable 'r'.

Reorder the terms:
-24 + -40 + -29r + 5r + 4r2 = 40 + -5r + -40 + 5r

Combine like terms: -24 + -40 = -64
-64 + -29r + 5r + 4r2 = 40 + -5r + -40 + 5r

Combine like terms: -29r + 5r = -24r
-64 + -24r + 4r2 = 40 + -5r + -40 + 5r

Reorder the terms:
-64 + -24r + 4r2 = 40 + -40 + -5r + 5r

Combine like terms: 40 + -40 = 0
-64 + -24r + 4r2 = 0 + -5r + 5r
-64 + -24r + 4r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
-64 + -24r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -6r + r2) = 0

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

Ignore the factor 4.

Subproblem 1
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 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 = {-2, 8}

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