(r-1)(4r+7)=0

Solution for (r-1)(4r+7)=0 equation:

Simplifying
(r + -1)(4r + 7) = 0

Reorder the terms:
(-1 + r)(4r + 7) = 0

Reorder the terms:
(-1 + r)(7 + 4r) = 0

Multiply (-1 + r) * (7 + 4r)
(-1(7 + 4r) + r(7 + 4r)) = 0
((7 * -1 + 4r * -1) + r(7 + 4r)) = 0
((-7 + -4r) + r(7 + 4r)) = 0
(-7 + -4r + (7 * r + 4r * r)) = 0
(-7 + -4r + (7r + 4r2)) = 0

Combine like terms: -4r + 7r = 3r
(-7 + 3r + 4r2) = 0

Solving
-7 + 3r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -4r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-7 + -4r)' equal to zero and attempt to solve:

Simplifying
-7 + -4r = 0

Solving
-7 + -4r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -4r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4r = 0 + 7
-4r = 0 + 7

Combine like terms: 0 + 7 = 7
-4r = 7

Divide each side by '-4'.
r = -1.75

Simplifying
r = -1.75
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-1.75, 1}