(x+7)(x+9)=(x+3)(x+21)

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Solution for (x+7)(x+9)=(x+3)(x+21) equation:


Simplifying
(x + 7)(x + 9) = (x + 3)(x + 21)

Reorder the terms:
(7 + x)(x + 9) = (x + 3)(x + 21)

Reorder the terms:
(7 + x)(9 + x) = (x + 3)(x + 21)

Multiply (7 + x) * (9 + x)
(7(9 + x) + x(9 + x)) = (x + 3)(x + 21)
((9 * 7 + x * 7) + x(9 + x)) = (x + 3)(x + 21)
((63 + 7x) + x(9 + x)) = (x + 3)(x + 21)
(63 + 7x + (9 * x + x * x)) = (x + 3)(x + 21)
(63 + 7x + (9x + x2)) = (x + 3)(x + 21)

Combine like terms: 7x + 9x = 16x
(63 + 16x + x2) = (x + 3)(x + 21)

Reorder the terms:
63 + 16x + x2 = (3 + x)(x + 21)

Reorder the terms:
63 + 16x + x2 = (3 + x)(21 + x)

Multiply (3 + x) * (21 + x)
63 + 16x + x2 = (3(21 + x) + x(21 + x))
63 + 16x + x2 = ((21 * 3 + x * 3) + x(21 + x))
63 + 16x + x2 = ((63 + 3x) + x(21 + x))
63 + 16x + x2 = (63 + 3x + (21 * x + x * x))
63 + 16x + x2 = (63 + 3x + (21x + x2))

Combine like terms: 3x + 21x = 24x
63 + 16x + x2 = (63 + 24x + x2)

Add '-63' to each side of the equation.
63 + 16x + -63 + x2 = 63 + 24x + -63 + x2

Reorder the terms:
63 + -63 + 16x + x2 = 63 + 24x + -63 + x2

Combine like terms: 63 + -63 = 0
0 + 16x + x2 = 63 + 24x + -63 + x2
16x + x2 = 63 + 24x + -63 + x2

Reorder the terms:
16x + x2 = 63 + -63 + 24x + x2

Combine like terms: 63 + -63 = 0
16x + x2 = 0 + 24x + x2
16x + x2 = 24x + x2

Add '-1x2' to each side of the equation.
16x + x2 + -1x2 = 24x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16x + 0 = 24x + x2 + -1x2
16x = 24x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16x = 24x + 0
16x = 24x

Solving
16x = 24x

Solving for variable 'x'.

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

Add '-24x' to each side of the equation.
16x + -24x = 24x + -24x

Combine like terms: 16x + -24x = -8x
-8x = 24x + -24x

Combine like terms: 24x + -24x = 0
-8x = 0

Divide each side by '-8'.
x = 0

Simplifying
x = 0

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