(x+2)(x^2-2x+4)+x(5-x)(x+5)=-17

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Solution for (x+2)(x^2-2x+4)+x(5-x)(x+5)=-17 equation: 


Simplifying
(x + 2)(x2 + -2x + 4) + x(5 + -1x)(x + 5) = -17

Reorder the terms:
(2 + x)(x2 + -2x + 4) + x(5 + -1x)(x + 5) = -17

Reorder the terms:
(2 + x)(4 + -2x + x2) + x(5 + -1x)(x + 5) = -17

Multiply (2 + x) * (4 + -2x + x2)
(2(4 + -2x + x2) + x(4 + -2x + x2)) + x(5 + -1x)(x + 5) = -17
((4 * 2 + -2x * 2 + x2 * 2) + x(4 + -2x + x2)) + x(5 + -1x)(x + 5) = -17
((8 + -4x + 2x2) + x(4 + -2x + x2)) + x(5 + -1x)(x + 5) = -17
(8 + -4x + 2x2 + (4 * x + -2x * x + x2 * x)) + x(5 + -1x)(x + 5) = -17
(8 + -4x + 2x2 + (4x + -2x2 + x3)) + x(5 + -1x)(x + 5) = -17

Reorder the terms:
(8 + -4x + 4x + 2x2 + -2x2 + x3) + x(5 + -1x)(x + 5) = -17

Combine like terms: -4x + 4x = 0
(8 + 0 + 2x2 + -2x2 + x3) + x(5 + -1x)(x + 5) = -17
(8 + 2x2 + -2x2 + x3) + x(5 + -1x)(x + 5) = -17

Combine like terms: 2x2 + -2x2 = 0
(8 + 0 + x3) + x(5 + -1x)(x + 5) = -17
(8 + x3) + x(5 + -1x)(x + 5) = -17

Reorder the terms:
8 + x3 + x(5 + -1x)(5 + x) = -17

Multiply (5 + -1x) * (5 + x)
8 + x3 + x(5(5 + x) + -1x * (5 + x)) = -17
8 + x3 + x((5 * 5 + x * 5) + -1x * (5 + x)) = -17
8 + x3 + x((25 + 5x) + -1x * (5 + x)) = -17
8 + x3 + x(25 + 5x + (5 * -1x + x * -1x)) = -17
8 + x3 + x(25 + 5x + (-5x + -1x2)) = -17

Combine like terms: 5x + -5x = 0
8 + x3 + x(25 + 0 + -1x2) = -17
8 + x3 + x(25 + -1x2) = -17
8 + x3 + (25 * x + -1x2 * x) = -17
8 + x3 + (25x + -1x3) = -17

Reorder the terms:
8 + 25x + x3 + -1x3 = -17

Combine like terms: x3 + -1x3 = 0
8 + 25x + 0 = -17
8 + 25x = -17

Solving
8 + 25x = -17

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + 25x = -17 + -8

Combine like terms: 8 + -8 = 0
0 + 25x = -17 + -8
25x = -17 + -8

Combine like terms: -17 + -8 = -25
25x = -25

Divide each side by '25'.
x = -1

Simplifying
x = -1

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