(v+2)(v-4)-7=0

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Solution for (v+2)(v-4)-7=0 equation:


Simplifying
(v + 2)(v + -4) + -7 = 0

Reorder the terms:
(2 + v)(v + -4) + -7 = 0

Reorder the terms:
(2 + v)(-4 + v) + -7 = 0

Multiply (2 + v) * (-4 + v)
(2(-4 + v) + v(-4 + v)) + -7 = 0
((-4 * 2 + v * 2) + v(-4 + v)) + -7 = 0
((-8 + 2v) + v(-4 + v)) + -7 = 0
(-8 + 2v + (-4 * v + v * v)) + -7 = 0
(-8 + 2v + (-4v + v2)) + -7 = 0

Combine like terms: 2v + -4v = -2v
(-8 + -2v + v2) + -7 = 0

Reorder the terms:
-8 + -7 + -2v + v2 = 0

Combine like terms: -8 + -7 = -15
-15 + -2v + v2 = 0

Solving
-15 + -2v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-3 + -1v)(5 + -1v) = 0

Subproblem 1

Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3

Subproblem 2

Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5

Solution

v = {-3, 5}

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