2u(2u-7)=18

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Solution for 2u(2u-7)=18 equation:


Simplifying
2u(2u + -7) = 18

Reorder the terms:
2u(-7 + 2u) = 18
(-7 * 2u + 2u * 2u) = 18
(-14u + 4u2) = 18

Solving
-14u + 4u2 = 18

Solving for variable 'u'.

Reorder the terms:
-18 + -14u + 4u2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -14u + 4u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -7u + 2u2) = 0

Factor a trinomial.
2((-1 + -1u)(9 + -2u)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(9 + -2u)' equal to zero and attempt to solve: Simplifying 9 + -2u = 0 Solving 9 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2u = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2u = 0 + -9 -2u = 0 + -9 Combine like terms: 0 + -9 = -9 -2u = -9 Divide each side by '-2'. u = 4.5 Simplifying u = 4.5

Solution

u = {-1, 4.5}

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