3x(x+3)=(2x-8)(x+3)

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Solution for 3x(x+3)=(2x-8)(x+3) equation:


Simplifying
3x(x + 3) = (2x + -8)(x + 3)

Reorder the terms:
3x(3 + x) = (2x + -8)(x + 3)
(3 * 3x + x * 3x) = (2x + -8)(x + 3)
(9x + 3x2) = (2x + -8)(x + 3)

Reorder the terms:
9x + 3x2 = (-8 + 2x)(x + 3)

Reorder the terms:
9x + 3x2 = (-8 + 2x)(3 + x)

Multiply (-8 + 2x) * (3 + x)
9x + 3x2 = (-8(3 + x) + 2x * (3 + x))
9x + 3x2 = ((3 * -8 + x * -8) + 2x * (3 + x))
9x + 3x2 = ((-24 + -8x) + 2x * (3 + x))
9x + 3x2 = (-24 + -8x + (3 * 2x + x * 2x))
9x + 3x2 = (-24 + -8x + (6x + 2x2))

Combine like terms: -8x + 6x = -2x
9x + 3x2 = (-24 + -2x + 2x2)

Solving
9x + 3x2 = -24 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
24 + 9x + 2x + 3x2 + -2x2 = -24 + -2x + 2x2 + 24 + 2x + -2x2

Combine like terms: 9x + 2x = 11x
24 + 11x + 3x2 + -2x2 = -24 + -2x + 2x2 + 24 + 2x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
24 + 11x + 1x2 = -24 + -2x + 2x2 + 24 + 2x + -2x2

Reorder the terms:
24 + 11x + 1x2 = -24 + 24 + -2x + 2x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
24 + 11x + 1x2 = 0 + -2x + 2x + 2x2 + -2x2
24 + 11x + 1x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
24 + 11x + 1x2 = 0 + 2x2 + -2x2
24 + 11x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + 11x + 1x2 = 0

Factor a trinomial.
(8 + x)(3 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

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 = {-8, -3}

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