(x-7)(x+8)=3(x-16)

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Solution for (x-7)(x+8)=3(x-16) equation: 


Simplifying
(x + -7)(x + 8) = 3(x + -16)

Reorder the terms:
(-7 + x)(x + 8) = 3(x + -16)

Reorder the terms:
(-7 + x)(8 + x) = 3(x + -16)

Multiply (-7 + x) * (8 + x)
(-7(8 + x) + x(8 + x)) = 3(x + -16)
((8 * -7 + x * -7) + x(8 + x)) = 3(x + -16)
((-56 + -7x) + x(8 + x)) = 3(x + -16)
(-56 + -7x + (8 * x + x * x)) = 3(x + -16)
(-56 + -7x + (8x + x2)) = 3(x + -16)

Combine like terms: -7x + 8x = 1x
(-56 + 1x + x2) = 3(x + -16)

Reorder the terms:
-56 + 1x + x2 = 3(-16 + x)
-56 + 1x + x2 = (-16 * 3 + x * 3)
-56 + 1x + x2 = (-48 + 3x)

Solving
-56 + 1x + x2 = -48 + 3x

Solving for variable 'x'.

Reorder the terms:
-56 + 48 + 1x + -3x + x2 = -48 + 3x + 48 + -3x

Combine like terms: -56 + 48 = -8
-8 + 1x + -3x + x2 = -48 + 3x + 48 + -3x

Combine like terms: 1x + -3x = -2x
-8 + -2x + x2 = -48 + 3x + 48 + -3x

Reorder the terms:
-8 + -2x + x2 = -48 + 48 + 3x + -3x

Combine like terms: -48 + 48 = 0
-8 + -2x + x2 = 0 + 3x + -3x
-8 + -2x + x2 = 3x + -3x

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

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}

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