x^2+3x-17=-8x-5

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Solution for x^2+3x-17=-8x-5 equation:


Simplifying
x2 + 3x + -17 = -8x + -5

Reorder the terms:
-17 + 3x + x2 = -8x + -5

Reorder the terms:
-17 + 3x + x2 = -5 + -8x

Solving
-17 + 3x + x2 = -5 + -8x

Solving for variable 'x'.

Reorder the terms:
-17 + 5 + 3x + 8x + x2 = -5 + -8x + 5 + 8x

Combine like terms: -17 + 5 = -12
-12 + 3x + 8x + x2 = -5 + -8x + 5 + 8x

Combine like terms: 3x + 8x = 11x
-12 + 11x + x2 = -5 + -8x + 5 + 8x

Reorder the terms:
-12 + 11x + x2 = -5 + 5 + -8x + 8x

Combine like terms: -5 + 5 = 0
-12 + 11x + x2 = 0 + -8x + 8x
-12 + 11x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-12 + 11x + x2 = 0

Factor a trinomial.
(-12 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-12, 1}

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