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

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Solution for 12(x+5)+x(x+3)=2(x+5)(x+3) equation: 


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

Reorder the terms:
12(5 + x) + x(x + 3) = 2(x + 5)(x + 3)
(5 * 12 + x * 12) + x(x + 3) = 2(x + 5)(x + 3)
(60 + 12x) + x(x + 3) = 2(x + 5)(x + 3)

Reorder the terms:
60 + 12x + x(3 + x) = 2(x + 5)(x + 3)
60 + 12x + (3 * x + x * x) = 2(x + 5)(x + 3)
60 + 12x + (3x + x2) = 2(x + 5)(x + 3)

Combine like terms: 12x + 3x = 15x
60 + 15x + x2 = 2(x + 5)(x + 3)

Reorder the terms:
60 + 15x + x2 = 2(5 + x)(x + 3)

Reorder the terms:
60 + 15x + x2 = 2(5 + x)(3 + x)

Multiply (5 + x) * (3 + x)
60 + 15x + x2 = 2(5(3 + x) + x(3 + x))
60 + 15x + x2 = 2((3 * 5 + x * 5) + x(3 + x))
60 + 15x + x2 = 2((15 + 5x) + x(3 + x))
60 + 15x + x2 = 2(15 + 5x + (3 * x + x * x))
60 + 15x + x2 = 2(15 + 5x + (3x + x2))

Combine like terms: 5x + 3x = 8x
60 + 15x + x2 = 2(15 + 8x + x2)
60 + 15x + x2 = (15 * 2 + 8x * 2 + x2 * 2)
60 + 15x + x2 = (30 + 16x + 2x2)

Solving
60 + 15x + x2 = 30 + 16x + 2x2

Solving for variable 'x'.

Reorder the terms:
60 + -30 + 15x + -16x + x2 + -2x2 = 30 + 16x + 2x2 + -30 + -16x + -2x2

Combine like terms: 60 + -30 = 30
30 + 15x + -16x + x2 + -2x2 = 30 + 16x + 2x2 + -30 + -16x + -2x2

Combine like terms: 15x + -16x = -1x
30 + -1x + x2 + -2x2 = 30 + 16x + 2x2 + -30 + -16x + -2x2

Combine like terms: x2 + -2x2 = -1x2
30 + -1x + -1x2 = 30 + 16x + 2x2 + -30 + -16x + -2x2

Reorder the terms:
30 + -1x + -1x2 = 30 + -30 + 16x + -16x + 2x2 + -2x2

Combine like terms: 30 + -30 = 0
30 + -1x + -1x2 = 0 + 16x + -16x + 2x2 + -2x2
30 + -1x + -1x2 = 16x + -16x + 2x2 + -2x2

Combine like terms: 16x + -16x = 0
30 + -1x + -1x2 = 0 + 2x2 + -2x2
30 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + -1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {5, -6}

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