-15r=14+4r-3r^2

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Solution for -15r=14+4r-3r^2 equation: 


Simplifying
-15r = 14 + 4r + -3r2

Solving
-15r = 14 + 4r + -3r2

Solving for variable 'r'.

Reorder the terms:
-14 + -15r + -4r + 3r2 = 14 + 4r + -3r2 + -14 + -4r + 3r2

Combine like terms: -15r + -4r = -19r
-14 + -19r + 3r2 = 14 + 4r + -3r2 + -14 + -4r + 3r2

Reorder the terms:
-14 + -19r + 3r2 = 14 + -14 + 4r + -4r + -3r2 + 3r2

Combine like terms: 14 + -14 = 0
-14 + -19r + 3r2 = 0 + 4r + -4r + -3r2 + 3r2
-14 + -19r + 3r2 = 4r + -4r + -3r2 + 3r2

Combine like terms: 4r + -4r = 0
-14 + -19r + 3r2 = 0 + -3r2 + 3r2
-14 + -19r + 3r2 = -3r2 + 3r2

Combine like terms: -3r2 + 3r2 = 0
-14 + -19r + 3r2 = 0

Factor a trinomial.
(-2 + -3r)(7 + -1r) = 0


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

Simplifying
-2 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667

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 = {-0.6666666667, 7}

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