(u-7)(u+4)=1(u-7)(u+2)+(u-5)(u+2)

Solution for (u-7)(u+4)=1(u-7)(u+2)+(u-5)(u+2) equation:

Simplifying
(u + -7)(u + 4) = 1(u + -7)(u + 2) + (u + -5)(u + 2)

Reorder the terms:
(-7 + u)(u + 4) = 1(u + -7)(u + 2) + (u + -5)(u + 2)

Reorder the terms:
(-7 + u)(4 + u) = 1(u + -7)(u + 2) + (u + -5)(u + 2)

Multiply (-7 + u) * (4 + u)
(-7(4 + u) + u(4 + u)) = 1(u + -7)(u + 2) + (u + -5)(u + 2)
((4 * -7 + u * -7) + u(4 + u)) = 1(u + -7)(u + 2) + (u + -5)(u + 2)
((-28 + -7u) + u(4 + u)) = 1(u + -7)(u + 2) + (u + -5)(u + 2)
(-28 + -7u + (4 * u + u * u)) = 1(u + -7)(u + 2) + (u + -5)(u + 2)
(-28 + -7u + (4u + u2)) = 1(u + -7)(u + 2) + (u + -5)(u + 2)

Combine like terms: -7u + 4u = -3u
(-28 + -3u + u2) = 1(u + -7)(u + 2) + (u + -5)(u + 2)

Reorder the terms:
-28 + -3u + u2 = 1(-7 + u)(u + 2) + (u + -5)(u + 2)

Reorder the terms:
-28 + -3u + u2 = 1(-7 + u)(2 + u) + (u + -5)(u + 2)

Multiply (-7 + u) * (2 + u)
-28 + -3u + u2 = 1(-7(2 + u) + u(2 + u)) + (u + -5)(u + 2)
-28 + -3u + u2 = 1((2 * -7 + u * -7) + u(2 + u)) + (u + -5)(u + 2)
-28 + -3u + u2 = 1((-14 + -7u) + u(2 + u)) + (u + -5)(u + 2)
-28 + -3u + u2 = 1(-14 + -7u + (2 * u + u * u)) + (u + -5)(u + 2)
-28 + -3u + u2 = 1(-14 + -7u + (2u + u2)) + (u + -5)(u + 2)

Combine like terms: -7u + 2u = -5u
-28 + -3u + u2 = 1(-14 + -5u + u2) + (u + -5)(u + 2)
-28 + -3u + u2 = (-14 * 1 + -5u * 1 + u2 * 1) + (u + -5)(u + 2)
-28 + -3u + u2 = (-14 + -5u + 1u2) + (u + -5)(u + 2)

Reorder the terms:
-28 + -3u + u2 = -14 + -5u + 1u2 + (-5 + u)(u + 2)

Reorder the terms:
-28 + -3u + u2 = -14 + -5u + 1u2 + (-5 + u)(2 + u)

Multiply (-5 + u) * (2 + u)
-28 + -3u + u2 = -14 + -5u + 1u2 + (-5(2 + u) + u(2 + u))
-28 + -3u + u2 = -14 + -5u + 1u2 + ((2 * -5 + u * -5) + u(2 + u))
-28 + -3u + u2 = -14 + -5u + 1u2 + ((-10 + -5u) + u(2 + u))
-28 + -3u + u2 = -14 + -5u + 1u2 + (-10 + -5u + (2 * u + u * u))
-28 + -3u + u2 = -14 + -5u + 1u2 + (-10 + -5u + (2u + u2))

Combine like terms: -5u + 2u = -3u
-28 + -3u + u2 = -14 + -5u + 1u2 + (-10 + -3u + u2)

Reorder the terms:
-28 + -3u + u2 = -14 + -10 + -5u + -3u + 1u2 + u2

Combine like terms: -14 + -10 = -24
-28 + -3u + u2 = -24 + -5u + -3u + 1u2 + u2

Combine like terms: -5u + -3u = -8u
-28 + -3u + u2 = -24 + -8u + 1u2 + u2

Combine like terms: 1u2 + u2 = 2u2
-28 + -3u + u2 = -24 + -8u + 2u2

Solving
-28 + -3u + u2 = -24 + -8u + 2u2

Solving for variable 'u'.

Reorder the terms:
-28 + 24 + -3u + 8u + u2 + -2u2 = -24 + -8u + 2u2 + 24 + 8u + -2u2

Combine like terms: -28 + 24 = -4
-4 + -3u + 8u + u2 + -2u2 = -24 + -8u + 2u2 + 24 + 8u + -2u2

Combine like terms: -3u + 8u = 5u
-4 + 5u + u2 + -2u2 = -24 + -8u + 2u2 + 24 + 8u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-4 + 5u + -1u2 = -24 + -8u + 2u2 + 24 + 8u + -2u2

Reorder the terms:
-4 + 5u + -1u2 = -24 + 24 + -8u + 8u + 2u2 + -2u2

Combine like terms: -24 + 24 = 0
-4 + 5u + -1u2 = 0 + -8u + 8u + 2u2 + -2u2
-4 + 5u + -1u2 = -8u + 8u + 2u2 + -2u2

Combine like terms: -8u + 8u = 0
-4 + 5u + -1u2 = 0 + 2u2 + -2u2
-4 + 5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-4 + 5u + -1u2 = 0

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

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

Simplifying
-4 + u = 0

Solving
-4 + u = 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 + u = 0 + 4

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

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

Simplifying
u = 4
Subproblem 2
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
Solution
u = {4, 1}