(r-4)(r+3)+(r-4)(r+2)=0

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Solution for (r-4)(r+3)+(r-4)(r+2)=0 equation:


Simplifying
(r + -4)(r + 3) + (r + -4)(r + 2) = 0

Reorder the terms:
(-4 + r)(r + 3) + (r + -4)(r + 2) = 0

Reorder the terms:
(-4 + r)(3 + r) + (r + -4)(r + 2) = 0

Multiply (-4 + r) * (3 + r)
(-4(3 + r) + r(3 + r)) + (r + -4)(r + 2) = 0
((3 * -4 + r * -4) + r(3 + r)) + (r + -4)(r + 2) = 0
((-12 + -4r) + r(3 + r)) + (r + -4)(r + 2) = 0
(-12 + -4r + (3 * r + r * r)) + (r + -4)(r + 2) = 0
(-12 + -4r + (3r + r2)) + (r + -4)(r + 2) = 0

Combine like terms: -4r + 3r = -1r
(-12 + -1r + r2) + (r + -4)(r + 2) = 0

Reorder the terms:
-12 + -1r + r2 + (-4 + r)(r + 2) = 0

Reorder the terms:
-12 + -1r + r2 + (-4 + r)(2 + r) = 0

Multiply (-4 + r) * (2 + r)
-12 + -1r + r2 + (-4(2 + r) + r(2 + r)) = 0
-12 + -1r + r2 + ((2 * -4 + r * -4) + r(2 + r)) = 0
-12 + -1r + r2 + ((-8 + -4r) + r(2 + r)) = 0
-12 + -1r + r2 + (-8 + -4r + (2 * r + r * r)) = 0
-12 + -1r + r2 + (-8 + -4r + (2r + r2)) = 0

Combine like terms: -4r + 2r = -2r
-12 + -1r + r2 + (-8 + -2r + r2) = 0

Reorder the terms:
-12 + -8 + -1r + -2r + r2 + r2 = 0

Combine like terms: -12 + -8 = -20
-20 + -1r + -2r + r2 + r2 = 0

Combine like terms: -1r + -2r = -3r
-20 + -3r + r2 + r2 = 0

Combine like terms: r2 + r2 = 2r2
-20 + -3r + 2r2 = 0

Solving
-20 + -3r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -2r)(4 + -1r) = 0

Subproblem 1

Set the factor '(-5 + -2r)' equal to zero and attempt to solve: Simplifying -5 + -2r = 0 Solving -5 + -2r = 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 + -2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r = 0 + 5 -2r = 0 + 5 Combine like terms: 0 + 5 = 5 -2r = 5 Divide each side by '-2'. r = -2.5 Simplifying r = -2.5

Subproblem 2

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

Solution

r = {-2.5, 4}

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