(x+1)*(x+1)=(x-2)*(x+7)

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Solution for (x+1)*(x+1)=(x-2)*(x+7) equation: 


Simplifying
(x + 1)(x + 1) = (x + -2)(x + 7)

Reorder the terms:
(1 + x)(x + 1) = (x + -2)(x + 7)

Reorder the terms:
(1 + x)(1 + x) = (x + -2)(x + 7)

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = (x + -2)(x + 7)
((1 * 1 + x * 1) + x(1 + x)) = (x + -2)(x + 7)
((1 + 1x) + x(1 + x)) = (x + -2)(x + 7)
(1 + 1x + (1 * x + x * x)) = (x + -2)(x + 7)
(1 + 1x + (1x + x2)) = (x + -2)(x + 7)

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = (x + -2)(x + 7)

Reorder the terms:
1 + 2x + x2 = (-2 + x)(x + 7)

Reorder the terms:
1 + 2x + x2 = (-2 + x)(7 + x)

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

Combine like terms: -2x + 7x = 5x
1 + 2x + x2 = (-14 + 5x + x2)

Add '-1x2' to each side of the equation.
1 + 2x + x2 + -1x2 = -14 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x + 0 = -14 + 5x + x2 + -1x2
1 + 2x = -14 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x = -14 + 5x + 0
1 + 2x = -14 + 5x

Solving
1 + 2x = -14 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
1 + 2x + -5x = -14 + 5x + -5x

Combine like terms: 2x + -5x = -3x
1 + -3x = -14 + 5x + -5x

Combine like terms: 5x + -5x = 0
1 + -3x = -14 + 0
1 + -3x = -14

Add '-1' to each side of the equation.
1 + -1 + -3x = -14 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = -14 + -1
-3x = -14 + -1

Combine like terms: -14 + -1 = -15
-3x = -15

Divide each side by '-3'.
x = 5

Simplifying
x = 5

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