(x-5)(x+8)=(x+4)(x-7)

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Solution for (x-5)(x+8)=(x+4)(x-7) equation: 


Simplifying
(x + -5)(x + 8) = (x + 4)(x + -7)

Reorder the terms:
(-5 + x)(x + 8) = (x + 4)(x + -7)

Reorder the terms:
(-5 + x)(8 + x) = (x + 4)(x + -7)

Multiply (-5 + x) * (8 + x)
(-5(8 + x) + x(8 + x)) = (x + 4)(x + -7)
((8 * -5 + x * -5) + x(8 + x)) = (x + 4)(x + -7)
((-40 + -5x) + x(8 + x)) = (x + 4)(x + -7)
(-40 + -5x + (8 * x + x * x)) = (x + 4)(x + -7)
(-40 + -5x + (8x + x2)) = (x + 4)(x + -7)

Combine like terms: -5x + 8x = 3x
(-40 + 3x + x2) = (x + 4)(x + -7)

Reorder the terms:
-40 + 3x + x2 = (4 + x)(x + -7)

Reorder the terms:
-40 + 3x + x2 = (4 + x)(-7 + x)

Multiply (4 + x) * (-7 + x)
-40 + 3x + x2 = (4(-7 + x) + x(-7 + x))
-40 + 3x + x2 = ((-7 * 4 + x * 4) + x(-7 + x))
-40 + 3x + x2 = ((-28 + 4x) + x(-7 + x))
-40 + 3x + x2 = (-28 + 4x + (-7 * x + x * x))
-40 + 3x + x2 = (-28 + 4x + (-7x + x2))

Combine like terms: 4x + -7x = -3x
-40 + 3x + x2 = (-28 + -3x + x2)

Add '-1x2' to each side of the equation.
-40 + 3x + x2 + -1x2 = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + 3x + 0 = -28 + -3x + x2 + -1x2
-40 + 3x = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + 3x = -28 + -3x + 0
-40 + 3x = -28 + -3x

Solving
-40 + 3x = -28 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-40 + 3x + 3x = -28 + -3x + 3x

Combine like terms: 3x + 3x = 6x
-40 + 6x = -28 + -3x + 3x

Combine like terms: -3x + 3x = 0
-40 + 6x = -28 + 0
-40 + 6x = -28

Add '40' to each side of the equation.
-40 + 40 + 6x = -28 + 40

Combine like terms: -40 + 40 = 0
0 + 6x = -28 + 40
6x = -28 + 40

Combine like terms: -28 + 40 = 12
6x = 12

Divide each side by '6'.
x = 2

Simplifying
x = 2

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