(x+8)(x-3)=(2x+7)(x-3)

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Solution for (x+8)(x-3)=(2x+7)(x-3) equation: 


Simplifying
(x + 8)(x + -3) = (2x + 7)(x + -3)

Reorder the terms:
(8 + x)(x + -3) = (2x + 7)(x + -3)

Reorder the terms:
(8 + x)(-3 + x) = (2x + 7)(x + -3)

Multiply (8 + x) * (-3 + x)
(8(-3 + x) + x(-3 + x)) = (2x + 7)(x + -3)
((-3 * 8 + x * 8) + x(-3 + x)) = (2x + 7)(x + -3)
((-24 + 8x) + x(-3 + x)) = (2x + 7)(x + -3)
(-24 + 8x + (-3 * x + x * x)) = (2x + 7)(x + -3)
(-24 + 8x + (-3x + x2)) = (2x + 7)(x + -3)

Combine like terms: 8x + -3x = 5x
(-24 + 5x + x2) = (2x + 7)(x + -3)

Reorder the terms:
-24 + 5x + x2 = (7 + 2x)(x + -3)

Reorder the terms:
-24 + 5x + x2 = (7 + 2x)(-3 + x)

Multiply (7 + 2x) * (-3 + x)
-24 + 5x + x2 = (7(-3 + x) + 2x * (-3 + x))
-24 + 5x + x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x))
-24 + 5x + x2 = ((-21 + 7x) + 2x * (-3 + x))
-24 + 5x + x2 = (-21 + 7x + (-3 * 2x + x * 2x))
-24 + 5x + x2 = (-21 + 7x + (-6x + 2x2))

Combine like terms: 7x + -6x = 1x
-24 + 5x + x2 = (-21 + 1x + 2x2)

Solving
-24 + 5x + x2 = -21 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-24 + 21 + 5x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: -24 + 21 = -3
-3 + 5x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: 5x + -1x = 4x
-3 + 4x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-3 + 4x + -1x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Reorder the terms:
-3 + 4x + -1x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
-3 + 4x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2
-3 + 4x + -1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
-3 + 4x + -1x2 = 0 + 2x2 + -2x2
-3 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 4x + -1x2 = 0

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


Subproblem 1
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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}

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