(x-2)(x+5)=(x-7)(x+4)

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Solution for (x-2)(x+5)=(x-7)(x+4) equation: 


Simplifying
(x + -2)(x + 5) = (x + -7)(x + 4)

Reorder the terms:
(-2 + x)(x + 5) = (x + -7)(x + 4)

Reorder the terms:
(-2 + x)(5 + x) = (x + -7)(x + 4)

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) = (x + -7)(x + 4)
((5 * -2 + x * -2) + x(5 + x)) = (x + -7)(x + 4)
((-10 + -2x) + x(5 + x)) = (x + -7)(x + 4)
(-10 + -2x + (5 * x + x * x)) = (x + -7)(x + 4)
(-10 + -2x + (5x + x2)) = (x + -7)(x + 4)

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) = (x + -7)(x + 4)

Reorder the terms:
-10 + 3x + x2 = (-7 + x)(x + 4)

Reorder the terms:
-10 + 3x + x2 = (-7 + x)(4 + x)

Multiply (-7 + x) * (4 + x)
-10 + 3x + x2 = (-7(4 + x) + x(4 + x))
-10 + 3x + x2 = ((4 * -7 + x * -7) + x(4 + x))
-10 + 3x + x2 = ((-28 + -7x) + x(4 + x))
-10 + 3x + x2 = (-28 + -7x + (4 * x + x * x))
-10 + 3x + x2 = (-28 + -7x + (4x + x2))

Combine like terms: -7x + 4x = -3x
-10 + 3x + x2 = (-28 + -3x + x2)

Add '-1x2' to each side of the equation.
-10 + 3x + x2 + -1x2 = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x + 0 = -28 + -3x + x2 + -1x2
-10 + 3x = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x = -28 + -3x + 0
-10 + 3x = -28 + -3x

Solving
-10 + 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.
-10 + 3x + 3x = -28 + -3x + 3x

Combine like terms: 3x + 3x = 6x
-10 + 6x = -28 + -3x + 3x

Combine like terms: -3x + 3x = 0
-10 + 6x = -28 + 0
-10 + 6x = -28

Add '10' to each side of the equation.
-10 + 10 + 6x = -28 + 10

Combine like terms: -10 + 10 = 0
0 + 6x = -28 + 10
6x = -28 + 10

Combine like terms: -28 + 10 = -18
6x = -18

Divide each side by '6'.
x = -3

Simplifying
x = -3

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