u(2u-7)=4(u-3)

Solution for u(2u-7)=4(u-3) equation:

Simplifying
u(2u + -7) = 4(u + -3)

Reorder the terms:
u(-7 + 2u) = 4(u + -3)
(-7 * u + 2u * u) = 4(u + -3)
(-7u + 2u2) = 4(u + -3)

Reorder the terms:
-7u + 2u2 = 4(-3 + u)
-7u + 2u2 = (-3 * 4 + u * 4)
-7u + 2u2 = (-12 + 4u)

Solving
-7u + 2u2 = -12 + 4u

Solving for variable 'u'.

Reorder the terms:
12 + -7u + -4u + 2u2 = -12 + 4u + 12 + -4u

Combine like terms: -7u + -4u = -11u
12 + -11u + 2u2 = -12 + 4u + 12 + -4u

Reorder the terms:
12 + -11u + 2u2 = -12 + 12 + 4u + -4u

Combine like terms: -12 + 12 = 0
12 + -11u + 2u2 = 0 + 4u + -4u
12 + -11u + 2u2 = 4u + -4u

Combine like terms: 4u + -4u = 0
12 + -11u + 2u2 = 0

Factor a trinomial.
(3 + -2u)(4 + -1u) = 0

Subproblem 1
Set the factor '(3 + -2u)' equal to zero and attempt to solve:

Simplifying
3 + -2u = 0

Solving
3 + -2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2u = 0 + -3
-2u = 0 + -3

Combine like terms: 0 + -3 = -3
-2u = -3

Divide each side by '-2'.
u = 1.5

Simplifying
u = 1.5
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {1.5, 4}