x^2+2x+4=7x-2

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Solution for x^2+2x+4=7x-2 equation:


Simplifying
x2 + 2x + 4 = 7x + -2

Reorder the terms:
4 + 2x + x2 = 7x + -2

Reorder the terms:
4 + 2x + x2 = -2 + 7x

Solving
4 + 2x + x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
4 + 2 + 2x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: 4 + 2 = 6
6 + 2x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: 2x + -7x = -5x
6 + -5x + x2 = -2 + 7x + 2 + -7x

Reorder the terms:
6 + -5x + x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
6 + -5x + x2 = 0 + 7x + -7x
6 + -5x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
6 + -5x + x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {2, 3}

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