x^2+19x+21=8x+3

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Solution for x^2+19x+21=8x+3 equation:


Simplifying
x2 + 19x + 21 = 8x + 3

Reorder the terms:
21 + 19x + x2 = 8x + 3

Reorder the terms:
21 + 19x + x2 = 3 + 8x

Solving
21 + 19x + x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
21 + -3 + 19x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: 21 + -3 = 18
18 + 19x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: 19x + -8x = 11x
18 + 11x + x2 = 3 + 8x + -3 + -8x

Reorder the terms:
18 + 11x + x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
18 + 11x + x2 = 0 + 8x + -8x
18 + 11x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
18 + 11x + x2 = 0

Factor a trinomial.
(9 + x)(2 + x) = 0

Subproblem 1

Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {-9, -2}

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