(u-2)(u+4)=(u+6)(u-3)

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Solution for (u-2)(u+4)=(u+6)(u-3) equation: 


Simplifying
(u + -2)(u + 4) = (u + 6)(u + -3)

Reorder the terms:
(-2 + u)(u + 4) = (u + 6)(u + -3)

Reorder the terms:
(-2 + u)(4 + u) = (u + 6)(u + -3)

Multiply (-2 + u) * (4 + u)
(-2(4 + u) + u(4 + u)) = (u + 6)(u + -3)
((4 * -2 + u * -2) + u(4 + u)) = (u + 6)(u + -3)
((-8 + -2u) + u(4 + u)) = (u + 6)(u + -3)
(-8 + -2u + (4 * u + u * u)) = (u + 6)(u + -3)
(-8 + -2u + (4u + u2)) = (u + 6)(u + -3)

Combine like terms: -2u + 4u = 2u
(-8 + 2u + u2) = (u + 6)(u + -3)

Reorder the terms:
-8 + 2u + u2 = (6 + u)(u + -3)

Reorder the terms:
-8 + 2u + u2 = (6 + u)(-3 + u)

Multiply (6 + u) * (-3 + u)
-8 + 2u + u2 = (6(-3 + u) + u(-3 + u))
-8 + 2u + u2 = ((-3 * 6 + u * 6) + u(-3 + u))
-8 + 2u + u2 = ((-18 + 6u) + u(-3 + u))
-8 + 2u + u2 = (-18 + 6u + (-3 * u + u * u))
-8 + 2u + u2 = (-18 + 6u + (-3u + u2))

Combine like terms: 6u + -3u = 3u
-8 + 2u + u2 = (-18 + 3u + u2)

Add '-1u2' to each side of the equation.
-8 + 2u + u2 + -1u2 = -18 + 3u + u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-8 + 2u + 0 = -18 + 3u + u2 + -1u2
-8 + 2u = -18 + 3u + u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-8 + 2u = -18 + 3u + 0
-8 + 2u = -18 + 3u

Solving
-8 + 2u = -18 + 3u

Solving for variable 'u'.

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

Add '-3u' to each side of the equation.
-8 + 2u + -3u = -18 + 3u + -3u

Combine like terms: 2u + -3u = -1u
-8 + -1u = -18 + 3u + -3u

Combine like terms: 3u + -3u = 0
-8 + -1u = -18 + 0
-8 + -1u = -18

Add '8' to each side of the equation.
-8 + 8 + -1u = -18 + 8

Combine like terms: -8 + 8 = 0
0 + -1u = -18 + 8
-1u = -18 + 8

Combine like terms: -18 + 8 = -10
-1u = -10

Divide each side by '-1'.
u = 10

Simplifying
u = 10

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