(x+2)(x-9)=x(5+x)

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


Simplifying
(x + 2)(x + -9) = x(5 + x)

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

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

Multiply (2 + x) * (-9 + x)
(2(-9 + x) + x(-9 + x)) = x(5 + x)
((-9 * 2 + x * 2) + x(-9 + x)) = x(5 + x)
((-18 + 2x) + x(-9 + x)) = x(5 + x)
(-18 + 2x + (-9 * x + x * x)) = x(5 + x)
(-18 + 2x + (-9x + x2)) = x(5 + x)

Combine like terms: 2x + -9x = -7x
(-18 + -7x + x2) = x(5 + x)
-18 + -7x + x2 = (5 * x + x * x)
-18 + -7x + x2 = (5x + x2)

Add '-1x2' to each side of the equation.
-18 + -7x + x2 + -1x2 = 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -7x + 0 = 5x + x2 + -1x2
-18 + -7x = 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -7x = 5x + 0
-18 + -7x = 5x

Solving
-18 + -7x = 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-18 + -7x + -5x = 5x + -5x

Combine like terms: -7x + -5x = -12x
-18 + -12x = 5x + -5x

Combine like terms: 5x + -5x = 0
-18 + -12x = 0

Add '18' to each side of the equation.
-18 + 18 + -12x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -12x = 0 + 18
-12x = 0 + 18

Combine like terms: 0 + 18 = 18
-12x = 18

Divide each side by '-12'.
x = -1.5

Simplifying
x = -1.5

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