x^2+21x+41=7x+1

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Solution for x^2+21x+41=7x+1 equation:


Simplifying
x2 + 21x + 41 = 7x + 1

Reorder the terms:
41 + 21x + x2 = 7x + 1

Reorder the terms:
41 + 21x + x2 = 1 + 7x

Solving
41 + 21x + x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
41 + -1 + 21x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: 41 + -1 = 40
40 + 21x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: 21x + -7x = 14x
40 + 14x + x2 = 1 + 7x + -1 + -7x

Reorder the terms:
40 + 14x + x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
40 + 14x + x2 = 0 + 7x + -7x
40 + 14x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
40 + 14x + x2 = 0

Factor a trinomial.
(10 + x)(4 + 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {-10, -4}

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