15x+(x+19)(x+19)=(x+16)(x+16)

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Solution for 15x+(x+19)(x+19)=(x+16)(x+16) equation: 


Simplifying
15x + (x + 19)(x + 19) = (x + 16)(x + 16)

Reorder the terms:
15x + (19 + x)(x + 19) = (x + 16)(x + 16)

Reorder the terms:
15x + (19 + x)(19 + x) = (x + 16)(x + 16)

Multiply (19 + x) * (19 + x)
15x + (19(19 + x) + x(19 + x)) = (x + 16)(x + 16)
15x + ((19 * 19 + x * 19) + x(19 + x)) = (x + 16)(x + 16)
15x + ((361 + 19x) + x(19 + x)) = (x + 16)(x + 16)
15x + (361 + 19x + (19 * x + x * x)) = (x + 16)(x + 16)
15x + (361 + 19x + (19x + x2)) = (x + 16)(x + 16)

Combine like terms: 19x + 19x = 38x
15x + (361 + 38x + x2) = (x + 16)(x + 16)

Reorder the terms:
361 + 15x + 38x + x2 = (x + 16)(x + 16)

Combine like terms: 15x + 38x = 53x
361 + 53x + x2 = (x + 16)(x + 16)

Reorder the terms:
361 + 53x + x2 = (16 + x)(x + 16)

Reorder the terms:
361 + 53x + x2 = (16 + x)(16 + x)

Multiply (16 + x) * (16 + x)
361 + 53x + x2 = (16(16 + x) + x(16 + x))
361 + 53x + x2 = ((16 * 16 + x * 16) + x(16 + x))
361 + 53x + x2 = ((256 + 16x) + x(16 + x))
361 + 53x + x2 = (256 + 16x + (16 * x + x * x))
361 + 53x + x2 = (256 + 16x + (16x + x2))

Combine like terms: 16x + 16x = 32x
361 + 53x + x2 = (256 + 32x + x2)

Add '-1x2' to each side of the equation.
361 + 53x + x2 + -1x2 = 256 + 32x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
361 + 53x + 0 = 256 + 32x + x2 + -1x2
361 + 53x = 256 + 32x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
361 + 53x = 256 + 32x + 0
361 + 53x = 256 + 32x

Solving
361 + 53x = 256 + 32x

Solving for variable 'x'.

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

Add '-32x' to each side of the equation.
361 + 53x + -32x = 256 + 32x + -32x

Combine like terms: 53x + -32x = 21x
361 + 21x = 256 + 32x + -32x

Combine like terms: 32x + -32x = 0
361 + 21x = 256 + 0
361 + 21x = 256

Add '-361' to each side of the equation.
361 + -361 + 21x = 256 + -361

Combine like terms: 361 + -361 = 0
0 + 21x = 256 + -361
21x = 256 + -361

Combine like terms: 256 + -361 = -105
21x = -105

Divide each side by '21'.
x = -5

Simplifying
x = -5

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