(x+4)(x-9)-4x=0

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Solution for (x+4)(x-9)-4x=0 equation: 


Simplifying
(x + 4)(x + -9) + -4x = 0

Reorder the terms:
(4 + x)(x + -9) + -4x = 0

Reorder the terms:
(4 + x)(-9 + x) + -4x = 0

Multiply (4 + x) * (-9 + x)
(4(-9 + x) + x(-9 + x)) + -4x = 0
((-9 * 4 + x * 4) + x(-9 + x)) + -4x = 0
((-36 + 4x) + x(-9 + x)) + -4x = 0
(-36 + 4x + (-9 * x + x * x)) + -4x = 0
(-36 + 4x + (-9x + x2)) + -4x = 0

Combine like terms: 4x + -9x = -5x
(-36 + -5x + x2) + -4x = 0

Reorder the terms:
-36 + -5x + -4x + x2 = 0

Combine like terms: -5x + -4x = -9x
-36 + -9x + x2 = 0

Solving
-36 + -9x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-3, 12}

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