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

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


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

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

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

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

Combine like terms: 8x + -2x = 6x
(-16 + 6x + x2) = (2x + 3)(x + -2)

Reorder the terms:
-16 + 6x + x2 = (3 + 2x)(x + -2)

Reorder the terms:
-16 + 6x + x2 = (3 + 2x)(-2 + x)

Multiply (3 + 2x) * (-2 + x)
-16 + 6x + x2 = (3(-2 + x) + 2x * (-2 + x))
-16 + 6x + x2 = ((-2 * 3 + x * 3) + 2x * (-2 + x))
-16 + 6x + x2 = ((-6 + 3x) + 2x * (-2 + x))
-16 + 6x + x2 = (-6 + 3x + (-2 * 2x + x * 2x))
-16 + 6x + x2 = (-6 + 3x + (-4x + 2x2))

Combine like terms: 3x + -4x = -1x
-16 + 6x + x2 = (-6 + -1x + 2x2)

Solving
-16 + 6x + x2 = -6 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + 6 + 6x + x + x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Combine like terms: -16 + 6 = -10
-10 + 6x + x + x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Combine like terms: 6x + x = 7x
-10 + 7x + x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-10 + 7x + -1x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Reorder the terms:
-10 + 7x + -1x2 = -6 + 6 + -1x + x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
-10 + 7x + -1x2 = 0 + -1x + x + 2x2 + -2x2
-10 + 7x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-10 + 7x + -1x2 = 0 + 2x2 + -2x2
-10 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 7x + -1x2 = 0

Factor a trinomial.
(-5 + x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {5, 2}

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