3r^2-5(r+1)=7r+58

Solution for 3r^2-5(r+1)=7r+58 equation:

Simplifying
3r2 + -5(r + 1) = 7r + 58

Reorder the terms:
3r2 + -5(1 + r) = 7r + 58
3r2 + (1 * -5 + r * -5) = 7r + 58
3r2 + (-5 + -5r) = 7r + 58

Reorder the terms:
-5 + -5r + 3r2 = 7r + 58

Reorder the terms:
-5 + -5r + 3r2 = 58 + 7r

Solving
-5 + -5r + 3r2 = 58 + 7r

Solving for variable 'r'.

Reorder the terms:
-5 + -58 + -5r + -7r + 3r2 = 58 + 7r + -58 + -7r

Combine like terms: -5 + -58 = -63
-63 + -5r + -7r + 3r2 = 58 + 7r + -58 + -7r

Combine like terms: -5r + -7r = -12r
-63 + -12r + 3r2 = 58 + 7r + -58 + -7r

Reorder the terms:
-63 + -12r + 3r2 = 58 + -58 + 7r + -7r

Combine like terms: 58 + -58 = 0
-63 + -12r + 3r2 = 0 + 7r + -7r
-63 + -12r + 3r2 = 7r + -7r

Combine like terms: 7r + -7r = 0
-63 + -12r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -4r + r2) = 0

Factor a trinomial.
3((-3 + -1r)(7 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 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 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-3, 7}