(V-5)(V+6)=12

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Solution for (V-5)(V+6)=12 equation:


Simplifying
(V + -5)(V + 6) = 12

Reorder the terms:
(-5 + V)(V + 6) = 12

Reorder the terms:
(-5 + V)(6 + V) = 12

Multiply (-5 + V) * (6 + V)
(-5(6 + V) + V(6 + V)) = 12
((6 * -5 + V * -5) + V(6 + V)) = 12
((-30 + -5V) + V(6 + V)) = 12
(-30 + -5V + (6 * V + V * V)) = 12
(-30 + -5V + (6V + V2)) = 12

Combine like terms: -5V + 6V = 1V
(-30 + 1V + V2) = 12

Solving
-30 + 1V + V2 = 12

Solving for variable 'V'.

Reorder the terms:
-30 + -12 + 1V + V2 = 12 + -12

Combine like terms: -30 + -12 = -42
-42 + 1V + V2 = 12 + -12

Combine like terms: 12 + -12 = 0
-42 + 1V + V2 = 0

Factor a trinomial.
(-7 + -1V)(6 + -1V) = 0

Subproblem 1

Set the factor '(-7 + -1V)' equal to zero and attempt to solve: Simplifying -7 + -1V = 0 Solving -7 + -1V = 0 Move all terms containing V to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1V = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1V = 0 + 7 -1V = 0 + 7 Combine like terms: 0 + 7 = 7 -1V = 7 Divide each side by '-1'. V = -7 Simplifying V = -7

Subproblem 2

Set the factor '(6 + -1V)' equal to zero and attempt to solve: Simplifying 6 + -1V = 0 Solving 6 + -1V = 0 Move all terms containing V to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1V = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1V = 0 + -6 -1V = 0 + -6 Combine like terms: 0 + -6 = -6 -1V = -6 Divide each side by '-1'. V = 6 Simplifying V = 6

Solution

V = {-7, 6}

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