(x+5)(x-3)=(x+4)(x+6)

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Solution for (x+5)(x-3)=(x+4)(x+6) equation: 


Simplifying
(x + 5)(x + -3) = (x + 4)(x + 6)

Reorder the terms:
(5 + x)(x + -3) = (x + 4)(x + 6)

Reorder the terms:
(5 + x)(-3 + x) = (x + 4)(x + 6)

Multiply (5 + x) * (-3 + x)
(5(-3 + x) + x(-3 + x)) = (x + 4)(x + 6)
((-3 * 5 + x * 5) + x(-3 + x)) = (x + 4)(x + 6)
((-15 + 5x) + x(-3 + x)) = (x + 4)(x + 6)
(-15 + 5x + (-3 * x + x * x)) = (x + 4)(x + 6)
(-15 + 5x + (-3x + x2)) = (x + 4)(x + 6)

Combine like terms: 5x + -3x = 2x
(-15 + 2x + x2) = (x + 4)(x + 6)

Reorder the terms:
-15 + 2x + x2 = (4 + x)(x + 6)

Reorder the terms:
-15 + 2x + x2 = (4 + x)(6 + x)

Multiply (4 + x) * (6 + x)
-15 + 2x + x2 = (4(6 + x) + x(6 + x))
-15 + 2x + x2 = ((6 * 4 + x * 4) + x(6 + x))
-15 + 2x + x2 = ((24 + 4x) + x(6 + x))
-15 + 2x + x2 = (24 + 4x + (6 * x + x * x))
-15 + 2x + x2 = (24 + 4x + (6x + x2))

Combine like terms: 4x + 6x = 10x
-15 + 2x + x2 = (24 + 10x + x2)

Add '-1x2' to each side of the equation.
-15 + 2x + x2 + -1x2 = 24 + 10x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 2x + 0 = 24 + 10x + x2 + -1x2
-15 + 2x = 24 + 10x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 2x = 24 + 10x + 0
-15 + 2x = 24 + 10x

Solving
-15 + 2x = 24 + 10x

Solving for variable 'x'.

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

Add '-10x' to each side of the equation.
-15 + 2x + -10x = 24 + 10x + -10x

Combine like terms: 2x + -10x = -8x
-15 + -8x = 24 + 10x + -10x

Combine like terms: 10x + -10x = 0
-15 + -8x = 24 + 0
-15 + -8x = 24

Add '15' to each side of the equation.
-15 + 15 + -8x = 24 + 15

Combine like terms: -15 + 15 = 0
0 + -8x = 24 + 15
-8x = 24 + 15

Combine like terms: 24 + 15 = 39
-8x = 39

Divide each side by '-8'.
x = -4.875

Simplifying
x = -4.875

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