(x-9)(x+5)=(x+4)(x+8)

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Solution for (x-9)(x+5)=(x+4)(x+8) equation: 


Simplifying
(x + -9)(x + 5) = (x + 4)(x + 8)

Reorder the terms:
(-9 + x)(x + 5) = (x + 4)(x + 8)

Reorder the terms:
(-9 + x)(5 + x) = (x + 4)(x + 8)

Multiply (-9 + x) * (5 + x)
(-9(5 + x) + x(5 + x)) = (x + 4)(x + 8)
((5 * -9 + x * -9) + x(5 + x)) = (x + 4)(x + 8)
((-45 + -9x) + x(5 + x)) = (x + 4)(x + 8)
(-45 + -9x + (5 * x + x * x)) = (x + 4)(x + 8)
(-45 + -9x + (5x + x2)) = (x + 4)(x + 8)

Combine like terms: -9x + 5x = -4x
(-45 + -4x + x2) = (x + 4)(x + 8)

Reorder the terms:
-45 + -4x + x2 = (4 + x)(x + 8)

Reorder the terms:
-45 + -4x + x2 = (4 + x)(8 + x)

Multiply (4 + x) * (8 + x)
-45 + -4x + x2 = (4(8 + x) + x(8 + x))
-45 + -4x + x2 = ((8 * 4 + x * 4) + x(8 + x))
-45 + -4x + x2 = ((32 + 4x) + x(8 + x))
-45 + -4x + x2 = (32 + 4x + (8 * x + x * x))
-45 + -4x + x2 = (32 + 4x + (8x + x2))

Combine like terms: 4x + 8x = 12x
-45 + -4x + x2 = (32 + 12x + x2)

Add '-1x2' to each side of the equation.
-45 + -4x + x2 + -1x2 = 32 + 12x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -4x + 0 = 32 + 12x + x2 + -1x2
-45 + -4x = 32 + 12x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -4x = 32 + 12x + 0
-45 + -4x = 32 + 12x

Solving
-45 + -4x = 32 + 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
-45 + -4x + -12x = 32 + 12x + -12x

Combine like terms: -4x + -12x = -16x
-45 + -16x = 32 + 12x + -12x

Combine like terms: 12x + -12x = 0
-45 + -16x = 32 + 0
-45 + -16x = 32

Add '45' to each side of the equation.
-45 + 45 + -16x = 32 + 45

Combine like terms: -45 + 45 = 0
0 + -16x = 32 + 45
-16x = 32 + 45

Combine like terms: 32 + 45 = 77
-16x = 77

Divide each side by '-16'.
x = -4.8125

Simplifying
x = -4.8125

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