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

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


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

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

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

Multiply (-7 + u) * (-4 + u)
(-7(-4 + u) + u(-4 + u)) = (u + -7)(2u + 3)
((-4 * -7 + u * -7) + u(-4 + u)) = (u + -7)(2u + 3)
((28 + -7u) + u(-4 + u)) = (u + -7)(2u + 3)
(28 + -7u + (-4 * u + u * u)) = (u + -7)(2u + 3)
(28 + -7u + (-4u + u2)) = (u + -7)(2u + 3)

Combine like terms: -7u + -4u = -11u
(28 + -11u + u2) = (u + -7)(2u + 3)

Reorder the terms:
28 + -11u + u2 = (-7 + u)(2u + 3)

Reorder the terms:
28 + -11u + u2 = (-7 + u)(3 + 2u)

Multiply (-7 + u) * (3 + 2u)
28 + -11u + u2 = (-7(3 + 2u) + u(3 + 2u))
28 + -11u + u2 = ((3 * -7 + 2u * -7) + u(3 + 2u))
28 + -11u + u2 = ((-21 + -14u) + u(3 + 2u))
28 + -11u + u2 = (-21 + -14u + (3 * u + 2u * u))
28 + -11u + u2 = (-21 + -14u + (3u + 2u2))

Combine like terms: -14u + 3u = -11u
28 + -11u + u2 = (-21 + -11u + 2u2)

Add '11u' to each side of the equation.
28 + -11u + 11u + u2 = -21 + -11u + 11u + 2u2

Combine like terms: -11u + 11u = 0
28 + 0 + u2 = -21 + -11u + 11u + 2u2
28 + u2 = -21 + -11u + 11u + 2u2

Combine like terms: -11u + 11u = 0
28 + u2 = -21 + 0 + 2u2
28 + u2 = -21 + 2u2

Solving
28 + u2 = -21 + 2u2

Solving for variable 'u'.

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

Add '-2u2' to each side of the equation.
28 + u2 + -2u2 = -21 + 2u2 + -2u2

Combine like terms: u2 + -2u2 = -1u2
28 + -1u2 = -21 + 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
28 + -1u2 = -21 + 0
28 + -1u2 = -21

Add '-28' to each side of the equation.
28 + -28 + -1u2 = -21 + -28

Combine like terms: 28 + -28 = 0
0 + -1u2 = -21 + -28
-1u2 = -21 + -28

Combine like terms: -21 + -28 = -49
-1u2 = -49

Divide each side by '-1'.
u2 = 49

Simplifying
u2 = 49

Take the square root of each side:
u = {-7, 7}

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