6u^2=19u-10

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Solution for 6u^2=19u-10 equation:


Simplifying
6u2 = 19u + -10

Reorder the terms:
6u2 = -10 + 19u

Solving
6u2 = -10 + 19u

Solving for variable 'u'.

Reorder the terms:
10 + -19u + 6u2 = -10 + 19u + 10 + -19u

Reorder the terms:
10 + -19u + 6u2 = -10 + 10 + 19u + -19u

Combine like terms: -10 + 10 = 0
10 + -19u + 6u2 = 0 + 19u + -19u
10 + -19u + 6u2 = 19u + -19u

Combine like terms: 19u + -19u = 0
10 + -19u + 6u2 = 0

Factor a trinomial.
(2 + -3u)(5 + -2u) = 0

Subproblem 1

Set the factor '(2 + -3u)' equal to zero and attempt to solve: Simplifying 2 + -3u = 0 Solving 2 + -3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3u = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3u = 0 + -2 -3u = 0 + -2 Combine like terms: 0 + -2 = -2 -3u = -2 Divide each side by '-3'. u = 0.6666666667 Simplifying u = 0.6666666667

Subproblem 2

Set the factor '(5 + -2u)' equal to zero and attempt to solve: Simplifying 5 + -2u = 0 Solving 5 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2u = 0 + -5 -2u = 0 + -5 Combine like terms: 0 + -5 = -5 -2u = -5 Divide each side by '-2'. u = 2.5 Simplifying u = 2.5

Solution

u = {0.6666666667, 2.5}

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