2x+6=(x+5)(x+3)

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Solution for 2x+6=(x+5)(x+3) equation:


Simplifying
2x + 6 = (x + 5)(x + 3)

Reorder the terms:
6 + 2x = (x + 5)(x + 3)

Reorder the terms:
6 + 2x = (5 + x)(x + 3)

Reorder the terms:
6 + 2x = (5 + x)(3 + x)

Multiply (5 + x) * (3 + x)
6 + 2x = (5(3 + x) + x(3 + x))
6 + 2x = ((3 * 5 + x * 5) + x(3 + x))
6 + 2x = ((15 + 5x) + x(3 + x))
6 + 2x = (15 + 5x + (3 * x + x * x))
6 + 2x = (15 + 5x + (3x + x2))

Combine like terms: 5x + 3x = 8x
6 + 2x = (15 + 8x + x2)

Solving
6 + 2x = 15 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
6 + -15 + 2x + -8x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2

Combine like terms: 6 + -15 = -9
-9 + 2x + -8x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2

Combine like terms: 2x + -8x = -6x
-9 + -6x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2

Reorder the terms:
-9 + -6x + -1x2 = 15 + -15 + 8x + -8x + x2 + -1x2

Combine like terms: 15 + -15 = 0
-9 + -6x + -1x2 = 0 + 8x + -8x + x2 + -1x2
-9 + -6x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-9 + -6x + -1x2 = 0 + x2 + -1x2
-9 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 6x + x2) = 0

Factor a trinomial.
-1((3 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-3, -3}

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