56v^2=48v+128

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Solution for 56v^2=48v+128 equation:


Simplifying
56v2 = 48v + 128

Reorder the terms:
56v2 = 128 + 48v

Solving
56v2 = 128 + 48v

Solving for variable 'v'.

Reorder the terms:
-128 + -48v + 56v2 = 128 + 48v + -128 + -48v

Reorder the terms:
-128 + -48v + 56v2 = 128 + -128 + 48v + -48v

Combine like terms: 128 + -128 = 0
-128 + -48v + 56v2 = 0 + 48v + -48v
-128 + -48v + 56v2 = 48v + -48v

Combine like terms: 48v + -48v = 0
-128 + -48v + 56v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-16 + -6v + 7v2) = 0

Factor a trinomial.
8((-8 + -7v)(2 + -1v)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-8 + -7v)' equal to zero and attempt to solve: Simplifying -8 + -7v = 0 Solving -8 + -7v = 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 + -7v = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7v = 0 + 8 -7v = 0 + 8 Combine like terms: 0 + 8 = 8 -7v = 8 Divide each side by '-7'. v = -1.142857143 Simplifying v = -1.142857143

Subproblem 2

Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2

Solution

v = {-1.142857143, 2}

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