x^2+19x=10x-8

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Solution for x^2+19x=10x-8 equation:


Simplifying
x2 + 19x = 10x + -8

Reorder the terms:
19x + x2 = 10x + -8

Reorder the terms:
19x + x2 = -8 + 10x

Solving
19x + x2 = -8 + 10x

Solving for variable 'x'.

Reorder the terms:
8 + 19x + -10x + x2 = -8 + 10x + 8 + -10x

Combine like terms: 19x + -10x = 9x
8 + 9x + x2 = -8 + 10x + 8 + -10x

Reorder the terms:
8 + 9x + x2 = -8 + 8 + 10x + -10x

Combine like terms: -8 + 8 = 0
8 + 9x + x2 = 0 + 10x + -10x
8 + 9x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
8 + 9x + x2 = 0

Factor a trinomial.
(8 + x)(1 + x) = 0

Subproblem 1

Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-8, -1}

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