(5+x)(2x+6)=(6+x)(5+x)

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Solution for (5+x)(2x+6)=(6+x)(5+x) equation:


Simplifying
(5 + x)(2x + 6) = (6 + x)(5 + x)

Reorder the terms:
(5 + x)(6 + 2x) = (6 + x)(5 + x)

Multiply (5 + x) * (6 + 2x)
(5(6 + 2x) + x(6 + 2x)) = (6 + x)(5 + x)
((6 * 5 + 2x * 5) + x(6 + 2x)) = (6 + x)(5 + x)
((30 + 10x) + x(6 + 2x)) = (6 + x)(5 + x)
(30 + 10x + (6 * x + 2x * x)) = (6 + x)(5 + x)
(30 + 10x + (6x + 2x2)) = (6 + x)(5 + x)

Combine like terms: 10x + 6x = 16x
(30 + 16x + 2x2) = (6 + x)(5 + x)

Multiply (6 + x) * (5 + x)
30 + 16x + 2x2 = (6(5 + x) + x(5 + x))
30 + 16x + 2x2 = ((5 * 6 + x * 6) + x(5 + x))
30 + 16x + 2x2 = ((30 + 6x) + x(5 + x))
30 + 16x + 2x2 = (30 + 6x + (5 * x + x * x))
30 + 16x + 2x2 = (30 + 6x + (5x + x2))

Combine like terms: 6x + 5x = 11x
30 + 16x + 2x2 = (30 + 11x + x2)

Add '-30' to each side of the equation.
30 + 16x + -30 + 2x2 = 30 + 11x + -30 + x2

Reorder the terms:
30 + -30 + 16x + 2x2 = 30 + 11x + -30 + x2

Combine like terms: 30 + -30 = 0
0 + 16x + 2x2 = 30 + 11x + -30 + x2
16x + 2x2 = 30 + 11x + -30 + x2

Reorder the terms:
16x + 2x2 = 30 + -30 + 11x + x2

Combine like terms: 30 + -30 = 0
16x + 2x2 = 0 + 11x + x2
16x + 2x2 = 11x + x2

Solving
16x + 2x2 = 11x + x2

Solving for variable 'x'.

Reorder the terms:
16x + -11x + 2x2 + -1x2 = 11x + x2 + -11x + -1x2

Combine like terms: 16x + -11x = 5x
5x + 2x2 + -1x2 = 11x + x2 + -11x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
5x + 1x2 = 11x + x2 + -11x + -1x2

Reorder the terms:
5x + 1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
5x + 1x2 = 0 + x2 + -1x2
5x + 1x2 = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {0, -5}

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