3x^2+71=2x^2-18x-9

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Solution for 3x^2+71=2x^2-18x-9 equation:


Simplifying
3x2 + 71 = 2x2 + -18x + -9

Reorder the terms:
71 + 3x2 = 2x2 + -18x + -9

Reorder the terms:
71 + 3x2 = -9 + -18x + 2x2

Solving
71 + 3x2 = -9 + -18x + 2x2

Solving for variable 'x'.

Reorder the terms:
71 + 9 + 18x + 3x2 + -2x2 = -9 + -18x + 2x2 + 9 + 18x + -2x2

Combine like terms: 71 + 9 = 80
80 + 18x + 3x2 + -2x2 = -9 + -18x + 2x2 + 9 + 18x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
80 + 18x + 1x2 = -9 + -18x + 2x2 + 9 + 18x + -2x2

Reorder the terms:
80 + 18x + 1x2 = -9 + 9 + -18x + 18x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
80 + 18x + 1x2 = 0 + -18x + 18x + 2x2 + -2x2
80 + 18x + 1x2 = -18x + 18x + 2x2 + -2x2

Combine like terms: -18x + 18x = 0
80 + 18x + 1x2 = 0 + 2x2 + -2x2
80 + 18x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
80 + 18x + 1x2 = 0

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

Subproblem 1

Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10

Subproblem 2

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

Solution

x = {-10, -8}

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