7v^2-53v-27=-3

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Solution for 7v^2-53v-27=-3 equation:


Simplifying
7v2 + -53v + -27 = -3

Reorder the terms:
-27 + -53v + 7v2 = -3

Solving
-27 + -53v + 7v2 = -3

Solving for variable 'v'.

Reorder the terms:
-27 + 3 + -53v + 7v2 = -3 + 3

Combine like terms: -27 + 3 = -24
-24 + -53v + 7v2 = -3 + 3

Combine like terms: -3 + 3 = 0
-24 + -53v + 7v2 = 0

Factor a trinomial.
(-3 + -7v)(8 + -1v) = 0

Subproblem 1

Set the factor '(-3 + -7v)' equal to zero and attempt to solve: Simplifying -3 + -7v = 0 Solving -3 + -7v = 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 + -7v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7v = 0 + 3 -7v = 0 + 3 Combine like terms: 0 + 3 = 3 -7v = 3 Divide each side by '-7'. v = -0.4285714286 Simplifying v = -0.4285714286

Subproblem 2

Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8

Solution

v = {-0.4285714286, 8}

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