(x+1)*(x+1)-2(3x+2)=(x-3)*(x-4)

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Solution for (x+1)*(x+1)-2(3x+2)=(x-3)*(x-4) equation:


Simplifying
(x + 1)(x + 1) + -2(3x + 2) = (x + -3)(x + -4)

Reorder the terms:
(1 + x)(x + 1) + -2(3x + 2) = (x + -3)(x + -4)

Reorder the terms:
(1 + x)(1 + x) + -2(3x + 2) = (x + -3)(x + -4)

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -2(3x + 2) = (x + -3)(x + -4)
((1 * 1 + x * 1) + x(1 + x)) + -2(3x + 2) = (x + -3)(x + -4)
((1 + 1x) + x(1 + x)) + -2(3x + 2) = (x + -3)(x + -4)
(1 + 1x + (1 * x + x * x)) + -2(3x + 2) = (x + -3)(x + -4)
(1 + 1x + (1x + x2)) + -2(3x + 2) = (x + -3)(x + -4)

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -2(3x + 2) = (x + -3)(x + -4)

Reorder the terms:
1 + 2x + x2 + -2(2 + 3x) = (x + -3)(x + -4)
1 + 2x + x2 + (2 * -2 + 3x * -2) = (x + -3)(x + -4)
1 + 2x + x2 + (-4 + -6x) = (x + -3)(x + -4)

Reorder the terms:
1 + -4 + 2x + -6x + x2 = (x + -3)(x + -4)

Combine like terms: 1 + -4 = -3
-3 + 2x + -6x + x2 = (x + -3)(x + -4)

Combine like terms: 2x + -6x = -4x
-3 + -4x + x2 = (x + -3)(x + -4)

Reorder the terms:
-3 + -4x + x2 = (-3 + x)(x + -4)

Reorder the terms:
-3 + -4x + x2 = (-3 + x)(-4 + x)

Multiply (-3 + x) * (-4 + x)
-3 + -4x + x2 = (-3(-4 + x) + x(-4 + x))
-3 + -4x + x2 = ((-4 * -3 + x * -3) + x(-4 + x))
-3 + -4x + x2 = ((12 + -3x) + x(-4 + x))
-3 + -4x + x2 = (12 + -3x + (-4 * x + x * x))
-3 + -4x + x2 = (12 + -3x + (-4x + x2))

Combine like terms: -3x + -4x = -7x
-3 + -4x + x2 = (12 + -7x + x2)

Add '-1x2' to each side of the equation.
-3 + -4x + x2 + -1x2 = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -4x + 0 = 12 + -7x + x2 + -1x2
-3 + -4x = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -4x = 12 + -7x + 0
-3 + -4x = 12 + -7x

Solving
-3 + -4x = 12 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
-3 + -4x + 7x = 12 + -7x + 7x

Combine like terms: -4x + 7x = 3x
-3 + 3x = 12 + -7x + 7x

Combine like terms: -7x + 7x = 0
-3 + 3x = 12 + 0
-3 + 3x = 12

Add '3' to each side of the equation.
-3 + 3 + 3x = 12 + 3

Combine like terms: -3 + 3 = 0
0 + 3x = 12 + 3
3x = 12 + 3

Combine like terms: 12 + 3 = 15
3x = 15

Divide each side by '3'.
x = 5

Simplifying
x = 5

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