x^2+x+7=6x+3

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Solution for x^2+x+7=6x+3 equation:


Simplifying
x2 + x + 7 = 6x + 3

Reorder the terms:
7 + x + x2 = 6x + 3

Reorder the terms:
7 + x + x2 = 3 + 6x

Solving
7 + x + x2 = 3 + 6x

Solving for variable 'x'.

Reorder the terms:
7 + -3 + x + -6x + x2 = 3 + 6x + -3 + -6x

Combine like terms: 7 + -3 = 4
4 + x + -6x + x2 = 3 + 6x + -3 + -6x

Combine like terms: x + -6x = -5x
4 + -5x + x2 = 3 + 6x + -3 + -6x

Reorder the terms:
4 + -5x + x2 = 3 + -3 + 6x + -6x

Combine like terms: 3 + -3 = 0
4 + -5x + x2 = 0 + 6x + -6x
4 + -5x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + -5x + x2 = 0

Factor a trinomial.
(1 + -1x)(4 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {1, 4}

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