(x+2)(x+5)=(x+3)2

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Solution for (x+2)(x+5)=(x+3)2 equation:


Simplifying
(x + 2)(x + 5) = (x + 3) * 2

Reorder the terms:
(2 + x)(x + 5) = (x + 3) * 2

Reorder the terms:
(2 + x)(5 + x) = (x + 3) * 2

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) = (x + 3) * 2
((5 * 2 + x * 2) + x(5 + x)) = (x + 3) * 2
((10 + 2x) + x(5 + x)) = (x + 3) * 2
(10 + 2x + (5 * x + x * x)) = (x + 3) * 2
(10 + 2x + (5x + x2)) = (x + 3) * 2

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) = (x + 3) * 2

Reorder the terms:
10 + 7x + x2 = (3 + x) * 2

Reorder the terms for easier multiplication:
10 + 7x + x2 = 2(3 + x)
10 + 7x + x2 = (3 * 2 + x * 2)
10 + 7x + x2 = (6 + 2x)

Solving
10 + 7x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
10 + -6 + 7x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 10 + -6 = 4
4 + 7x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 7x + -2x = 5x
4 + 5x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
4 + 5x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
4 + 5x + x2 = 0 + 2x + -2x
4 + 5x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + 5x + x2 = 0

Factor a trinomial.
(4 + x)(1 + x) = 0

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-4, -1}

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