7v(v-7)=13v+9

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Solution for 7v(v-7)=13v+9 equation:


Simplifying
7v(v + -7) = 13v + 9

Reorder the terms:
7v(-7 + v) = 13v + 9
(-7 * 7v + v * 7v) = 13v + 9
(-49v + 7v2) = 13v + 9

Reorder the terms:
-49v + 7v2 = 9 + 13v

Solving
-49v + 7v2 = 9 + 13v

Solving for variable 'v'.

Reorder the terms:
-9 + -49v + -13v + 7v2 = 9 + 13v + -9 + -13v

Combine like terms: -49v + -13v = -62v
-9 + -62v + 7v2 = 9 + 13v + -9 + -13v

Reorder the terms:
-9 + -62v + 7v2 = 9 + -9 + 13v + -13v

Combine like terms: 9 + -9 = 0
-9 + -62v + 7v2 = 0 + 13v + -13v
-9 + -62v + 7v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
-9 + -62v + 7v2 = 0

Factor a trinomial.
(-1 + -7v)(9 + -1v) = 0

Subproblem 1

Set the factor '(-1 + -7v)' equal to zero and attempt to solve: Simplifying -1 + -7v = 0 Solving -1 + -7v = 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 + -7v = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7v = 0 + 1 -7v = 0 + 1 Combine like terms: 0 + 1 = 1 -7v = 1 Divide each side by '-7'. v = -0.1428571429 Simplifying v = -0.1428571429

Subproblem 2

Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9

Solution

v = {-0.1428571429, 9}

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