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

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


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

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

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

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

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

Reorder the terms:
-14 + 5x + x2 = (1 + x)(x + 1)

Reorder the terms:
-14 + 5x + x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
-14 + 5x + x2 = (1(1 + x) + x(1 + x))
-14 + 5x + x2 = ((1 * 1 + x * 1) + x(1 + x))
-14 + 5x + x2 = ((1 + 1x) + x(1 + x))
-14 + 5x + x2 = (1 + 1x + (1 * x + x * x))
-14 + 5x + x2 = (1 + 1x + (1x + x2))

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

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

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

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

Solving
-14 + 5x = 1 + 2x

Solving for variable 'x'.

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

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

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

Combine like terms: 2x + -2x = 0
-14 + 3x = 1 + 0
-14 + 3x = 1

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

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

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

Divide each side by '3'.
x = 5

Simplifying
x = 5

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