x^2+3x=2x+6

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


Simplifying
x2 + 3x = 2x + 6

Reorder the terms:
3x + x2 = 2x + 6

Reorder the terms:
3x + x2 = 6 + 2x

Solving
3x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 3x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 3x + -2x = 1x
-6 + 1x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-6 + 1x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-6 + 1x + x2 = 0 + 2x + -2x
-6 + 1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + 1x + x2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-3, 2}

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