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

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


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

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

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

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

Combine like terms: 8x + -3x = 5x
(-24 + 5x + x2) = (2x + 3)(x + -3)

Reorder the terms:
-24 + 5x + x2 = (3 + 2x)(x + -3)

Reorder the terms:
-24 + 5x + x2 = (3 + 2x)(-3 + x)

Multiply (3 + 2x) * (-3 + x)
-24 + 5x + x2 = (3(-3 + x) + 2x * (-3 + x))
-24 + 5x + x2 = ((-3 * 3 + x * 3) + 2x * (-3 + x))
-24 + 5x + x2 = ((-9 + 3x) + 2x * (-3 + x))
-24 + 5x + x2 = (-9 + 3x + (-3 * 2x + x * 2x))
-24 + 5x + x2 = (-9 + 3x + (-6x + 2x2))

Combine like terms: 3x + -6x = -3x
-24 + 5x + x2 = (-9 + -3x + 2x2)

Solving
-24 + 5x + x2 = -9 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-24 + 9 + 5x + 3x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

Combine like terms: -24 + 9 = -15
-15 + 5x + 3x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

Combine like terms: 5x + 3x = 8x
-15 + 8x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2

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

Reorder the terms:
-15 + 8x + -1x2 = -9 + 9 + -3x + 3x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
-15 + 8x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
-15 + 8x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-15 + 8x + -1x2 = 0 + 2x2 + -2x2
-15 + 8x + -1x2 = 2x2 + -2x2

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

Factor a trinomial.
(-5 + x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {5, 3}

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