(3r+7)(3r-2)=0

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Solution for (3r+7)(3r-2)=0 equation: 


Simplifying
(3r + 7)(3r + -2) = 0

Reorder the terms:
(7 + 3r)(3r + -2) = 0

Reorder the terms:
(7 + 3r)(-2 + 3r) = 0

Multiply (7 + 3r) * (-2 + 3r)
(7(-2 + 3r) + 3r * (-2 + 3r)) = 0
((-2 * 7 + 3r * 7) + 3r * (-2 + 3r)) = 0
((-14 + 21r) + 3r * (-2 + 3r)) = 0
(-14 + 21r + (-2 * 3r + 3r * 3r)) = 0
(-14 + 21r + (-6r + 9r2)) = 0

Combine like terms: 21r + -6r = 15r
(-14 + 15r + 9r2) = 0

Solving
-14 + 15r + 9r2 = 0

Solving for variable 'r'.

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


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

Simplifying
-7 + -3r = 0

Solving
-7 + -3r = 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 + -3r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3r = 0 + 7
-3r = 0 + 7

Combine like terms: 0 + 7 = 7
-3r = 7

Divide each side by '-3'.
r = -2.333333333

Simplifying
r = -2.333333333

Subproblem 2
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
Solution
r = {-2.333333333, 0.6666666667}

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