2x^2+3x=x^2+18

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Solution for 2x^2+3x=x^2+18 equation:


Simplifying
2x2 + 3x = x2 + 18

Reorder the terms:
3x + 2x2 = x2 + 18

Reorder the terms:
3x + 2x2 = 18 + x2

Solving
3x + 2x2 = 18 + x2

Solving for variable 'x'.

Reorder the terms:
-18 + 3x + 2x2 + -1x2 = 18 + x2 + -18 + -1x2

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

Reorder the terms:
-18 + 3x + 1x2 = 18 + -18 + x2 + -1x2

Combine like terms: 18 + -18 = 0
-18 + 3x + 1x2 = 0 + x2 + -1x2
-18 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 3x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

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 = {-6, 3}

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