x^2-9x+20=(x-4)(x+5)

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Solution for x^2-9x+20=(x-4)(x+5) equation:


Simplifying
x2 + -9x + 20 = (x + -4)(x + 5)

Reorder the terms:
20 + -9x + x2 = (x + -4)(x + 5)

Reorder the terms:
20 + -9x + x2 = (-4 + x)(x + 5)

Reorder the terms:
20 + -9x + x2 = (-4 + x)(5 + x)

Multiply (-4 + x) * (5 + x)
20 + -9x + x2 = (-4(5 + x) + x(5 + x))
20 + -9x + x2 = ((5 * -4 + x * -4) + x(5 + x))
20 + -9x + x2 = ((-20 + -4x) + x(5 + x))
20 + -9x + x2 = (-20 + -4x + (5 * x + x * x))
20 + -9x + x2 = (-20 + -4x + (5x + x2))

Combine like terms: -4x + 5x = 1x
20 + -9x + x2 = (-20 + 1x + x2)

Add '-1x2' to each side of the equation.
20 + -9x + x2 + -1x2 = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -9x + 0 = -20 + 1x + x2 + -1x2
20 + -9x = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -9x = -20 + 1x + 0
20 + -9x = -20 + 1x

Solving
20 + -9x = -20 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
20 + -9x + -1x = -20 + 1x + -1x

Combine like terms: -9x + -1x = -10x
20 + -10x = -20 + 1x + -1x

Combine like terms: 1x + -1x = 0
20 + -10x = -20 + 0
20 + -10x = -20

Add '-20' to each side of the equation.
20 + -20 + -10x = -20 + -20

Combine like terms: 20 + -20 = 0
0 + -10x = -20 + -20
-10x = -20 + -20

Combine like terms: -20 + -20 = -40
-10x = -40

Divide each side by '-10'.
x = 4

Simplifying
x = 4

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