3x(x+8)=(2x-1)(x+8)

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Solution for 3x(x+8)=(2x-1)(x+8) equation: 


Simplifying
3x(x + 8) = (2x + -1)(x + 8)

Reorder the terms:
3x(8 + x) = (2x + -1)(x + 8)
(8 * 3x + x * 3x) = (2x + -1)(x + 8)
(24x + 3x2) = (2x + -1)(x + 8)

Reorder the terms:
24x + 3x2 = (-1 + 2x)(x + 8)

Reorder the terms:
24x + 3x2 = (-1 + 2x)(8 + x)

Multiply (-1 + 2x) * (8 + x)
24x + 3x2 = (-1(8 + x) + 2x * (8 + x))
24x + 3x2 = ((8 * -1 + x * -1) + 2x * (8 + x))
24x + 3x2 = ((-8 + -1x) + 2x * (8 + x))
24x + 3x2 = (-8 + -1x + (8 * 2x + x * 2x))
24x + 3x2 = (-8 + -1x + (16x + 2x2))

Combine like terms: -1x + 16x = 15x
24x + 3x2 = (-8 + 15x + 2x2)

Solving
24x + 3x2 = -8 + 15x + 2x2

Solving for variable 'x'.

Reorder the terms:
8 + 24x + -15x + 3x2 + -2x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Combine like terms: 24x + -15x = 9x
8 + 9x + 3x2 + -2x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
8 + 9x + 1x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Reorder the terms:
8 + 9x + 1x2 = -8 + 8 + 15x + -15x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
8 + 9x + 1x2 = 0 + 15x + -15x + 2x2 + -2x2
8 + 9x + 1x2 = 15x + -15x + 2x2 + -2x2

Combine like terms: 15x + -15x = 0
8 + 9x + 1x2 = 0 + 2x2 + -2x2
8 + 9x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + 9x + 1x2 = 0

Factor a trinomial.
(8 + x)(1 + 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 '(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 = {-8, -1}

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