7(v^2+5v-6)=0

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Solution for 7(v^2+5v-6)=0 equation:


Simplifying
7(v2 + 5v + -6) = 0

Reorder the terms:
7(-6 + 5v + v2) = 0
(-6 * 7 + 5v * 7 + v2 * 7) = 0
(-42 + 35v + 7v2) = 0

Solving
-42 + 35v + 7v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 5v + v2) = 0

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

Ignore the factor 7.

Subproblem 1

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

Subproblem 2

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

Solution

v = {-6, 1}

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