(7-x)*(7-x)+(14-x)*(7-2x)=(21-x)*(7-3x)

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Solution for (7-x)*(7-x)+(14-x)*(7-2x)=(21-x)*(7-3x) equation: 


Simplifying
(7 + -1x)(7 + -1x) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)

Multiply (7 + -1x) * (7 + -1x)
(7(7 + -1x) + -1x * (7 + -1x)) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)
((7 * 7 + -1x * 7) + -1x * (7 + -1x)) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)
((49 + -7x) + -1x * (7 + -1x)) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)
(49 + -7x + (7 * -1x + -1x * -1x)) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)
(49 + -7x + (-7x + 1x2)) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)

Combine like terms: -7x + -7x = -14x
(49 + -14x + 1x2) + (14 + -1x)(7 + -2x) = (21 + -1x)(7 + -3x)

Multiply (14 + -1x) * (7 + -2x)
49 + -14x + 1x2 + (14(7 + -2x) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x)
49 + -14x + 1x2 + ((7 * 14 + -2x * 14) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x)
49 + -14x + 1x2 + ((98 + -28x) + -1x * (7 + -2x)) = (21 + -1x)(7 + -3x)
49 + -14x + 1x2 + (98 + -28x + (7 * -1x + -2x * -1x)) = (21 + -1x)(7 + -3x)
49 + -14x + 1x2 + (98 + -28x + (-7x + 2x2)) = (21 + -1x)(7 + -3x)

Combine like terms: -28x + -7x = -35x
49 + -14x + 1x2 + (98 + -35x + 2x2) = (21 + -1x)(7 + -3x)

Reorder the terms:
49 + 98 + -14x + -35x + 1x2 + 2x2 = (21 + -1x)(7 + -3x)

Combine like terms: 49 + 98 = 147
147 + -14x + -35x + 1x2 + 2x2 = (21 + -1x)(7 + -3x)

Combine like terms: -14x + -35x = -49x
147 + -49x + 1x2 + 2x2 = (21 + -1x)(7 + -3x)

Combine like terms: 1x2 + 2x2 = 3x2
147 + -49x + 3x2 = (21 + -1x)(7 + -3x)

Multiply (21 + -1x) * (7 + -3x)
147 + -49x + 3x2 = (21(7 + -3x) + -1x * (7 + -3x))
147 + -49x + 3x2 = ((7 * 21 + -3x * 21) + -1x * (7 + -3x))
147 + -49x + 3x2 = ((147 + -63x) + -1x * (7 + -3x))
147 + -49x + 3x2 = (147 + -63x + (7 * -1x + -3x * -1x))
147 + -49x + 3x2 = (147 + -63x + (-7x + 3x2))

Combine like terms: -63x + -7x = -70x
147 + -49x + 3x2 = (147 + -70x + 3x2)

Add '-147' to each side of the equation.
147 + -49x + -147 + 3x2 = 147 + -70x + -147 + 3x2

Reorder the terms:
147 + -147 + -49x + 3x2 = 147 + -70x + -147 + 3x2

Combine like terms: 147 + -147 = 0
0 + -49x + 3x2 = 147 + -70x + -147 + 3x2
-49x + 3x2 = 147 + -70x + -147 + 3x2

Reorder the terms:
-49x + 3x2 = 147 + -147 + -70x + 3x2

Combine like terms: 147 + -147 = 0
-49x + 3x2 = 0 + -70x + 3x2
-49x + 3x2 = -70x + 3x2

Add '-3x2' to each side of the equation.
-49x + 3x2 + -3x2 = -70x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-49x + 0 = -70x + 3x2 + -3x2
-49x = -70x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-49x = -70x + 0
-49x = -70x

Solving
-49x = -70x

Solving for variable 'x'.

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

Add '70x' to each side of the equation.
-49x + 70x = -70x + 70x

Combine like terms: -49x + 70x = 21x
21x = -70x + 70x

Combine like terms: -70x + 70x = 0
21x = 0

Divide each side by '21'.
x = 0

Simplifying
x = 0

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