(x-1)(x+4)=(x-4)(x+9)

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Solution for (x-1)(x+4)=(x-4)(x+9) equation: 


Simplifying
(x + -1)(x + 4) = (x + -4)(x + 9)

Reorder the terms:
(-1 + x)(x + 4) = (x + -4)(x + 9)

Reorder the terms:
(-1 + x)(4 + x) = (x + -4)(x + 9)

Multiply (-1 + x) * (4 + x)
(-1(4 + x) + x(4 + x)) = (x + -4)(x + 9)
((4 * -1 + x * -1) + x(4 + x)) = (x + -4)(x + 9)
((-4 + -1x) + x(4 + x)) = (x + -4)(x + 9)
(-4 + -1x + (4 * x + x * x)) = (x + -4)(x + 9)
(-4 + -1x + (4x + x2)) = (x + -4)(x + 9)

Combine like terms: -1x + 4x = 3x
(-4 + 3x + x2) = (x + -4)(x + 9)

Reorder the terms:
-4 + 3x + x2 = (-4 + x)(x + 9)

Reorder the terms:
-4 + 3x + x2 = (-4 + x)(9 + x)

Multiply (-4 + x) * (9 + x)
-4 + 3x + x2 = (-4(9 + x) + x(9 + x))
-4 + 3x + x2 = ((9 * -4 + x * -4) + x(9 + x))
-4 + 3x + x2 = ((-36 + -4x) + x(9 + x))
-4 + 3x + x2 = (-36 + -4x + (9 * x + x * x))
-4 + 3x + x2 = (-36 + -4x + (9x + x2))

Combine like terms: -4x + 9x = 5x
-4 + 3x + x2 = (-36 + 5x + x2)

Add '-1x2' to each side of the equation.
-4 + 3x + x2 + -1x2 = -36 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x + 0 = -36 + 5x + x2 + -1x2
-4 + 3x = -36 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 3x = -36 + 5x + 0
-4 + 3x = -36 + 5x

Solving
-4 + 3x = -36 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-4 + 3x + -5x = -36 + 5x + -5x

Combine like terms: 3x + -5x = -2x
-4 + -2x = -36 + 5x + -5x

Combine like terms: 5x + -5x = 0
-4 + -2x = -36 + 0
-4 + -2x = -36

Add '4' to each side of the equation.
-4 + 4 + -2x = -36 + 4

Combine like terms: -4 + 4 = 0
0 + -2x = -36 + 4
-2x = -36 + 4

Combine like terms: -36 + 4 = -32
-2x = -32

Divide each side by '-2'.
x = 16

Simplifying
x = 16

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