(x+5)(x-9)=(x-4)(x-3)

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Solution for (x+5)(x-9)=(x-4)(x-3) equation: 


Simplifying
(x + 5)(x + -9) = (x + -4)(x + -3)

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

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

Multiply (5 + x) * (-9 + x)
(5(-9 + x) + x(-9 + x)) = (x + -4)(x + -3)
((-9 * 5 + x * 5) + x(-9 + x)) = (x + -4)(x + -3)
((-45 + 5x) + x(-9 + x)) = (x + -4)(x + -3)
(-45 + 5x + (-9 * x + x * x)) = (x + -4)(x + -3)
(-45 + 5x + (-9x + x2)) = (x + -4)(x + -3)

Combine like terms: 5x + -9x = -4x
(-45 + -4x + x2) = (x + -4)(x + -3)

Reorder the terms:
-45 + -4x + x2 = (-4 + x)(x + -3)

Reorder the terms:
-45 + -4x + x2 = (-4 + x)(-3 + x)

Multiply (-4 + x) * (-3 + x)
-45 + -4x + x2 = (-4(-3 + x) + x(-3 + x))
-45 + -4x + x2 = ((-3 * -4 + x * -4) + x(-3 + x))
-45 + -4x + x2 = ((12 + -4x) + x(-3 + x))
-45 + -4x + x2 = (12 + -4x + (-3 * x + x * x))
-45 + -4x + x2 = (12 + -4x + (-3x + x2))

Combine like terms: -4x + -3x = -7x
-45 + -4x + x2 = (12 + -7x + x2)

Add '-1x2' to each side of the equation.
-45 + -4x + x2 + -1x2 = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -4x + 0 = 12 + -7x + x2 + -1x2
-45 + -4x = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -4x = 12 + -7x + 0
-45 + -4x = 12 + -7x

Solving
-45 + -4x = 12 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
-45 + -4x + 7x = 12 + -7x + 7x

Combine like terms: -4x + 7x = 3x
-45 + 3x = 12 + -7x + 7x

Combine like terms: -7x + 7x = 0
-45 + 3x = 12 + 0
-45 + 3x = 12

Add '45' to each side of the equation.
-45 + 45 + 3x = 12 + 45

Combine like terms: -45 + 45 = 0
0 + 3x = 12 + 45
3x = 12 + 45

Combine like terms: 12 + 45 = 57
3x = 57

Divide each side by '3'.
x = 19

Simplifying
x = 19

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