(x+4)(x-12)-5x=0

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Solution for (x+4)(x-12)-5x=0 equation:


Simplifying
(x + 4)(x + -12) + -5x = 0

Reorder the terms:
(4 + x)(x + -12) + -5x = 0

Reorder the terms:
(4 + x)(-12 + x) + -5x = 0

Multiply (4 + x) * (-12 + x)
(4(-12 + x) + x(-12 + x)) + -5x = 0
((-12 * 4 + x * 4) + x(-12 + x)) + -5x = 0
((-48 + 4x) + x(-12 + x)) + -5x = 0
(-48 + 4x + (-12 * x + x * x)) + -5x = 0
(-48 + 4x + (-12x + x2)) + -5x = 0

Combine like terms: 4x + -12x = -8x
(-48 + -8x + x2) + -5x = 0

Reorder the terms:
-48 + -8x + -5x + x2 = 0

Combine like terms: -8x + -5x = -13x
-48 + -13x + x2 = 0

Solving
-48 + -13x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(16 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-3, 16}

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