2x^2+11x=2x+18

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Solution for 2x^2+11x=2x+18 equation:


Simplifying
2x2 + 11x = 2x + 18

Reorder the terms:
11x + 2x2 = 2x + 18

Reorder the terms:
11x + 2x2 = 18 + 2x

Solving
11x + 2x2 = 18 + 2x

Solving for variable 'x'.

Reorder the terms:
-18 + 11x + -2x + 2x2 = 18 + 2x + -18 + -2x

Combine like terms: 11x + -2x = 9x
-18 + 9x + 2x2 = 18 + 2x + -18 + -2x

Reorder the terms:
-18 + 9x + 2x2 = 18 + -18 + 2x + -2x

Combine like terms: 18 + -18 = 0
-18 + 9x + 2x2 = 0 + 2x + -2x
-18 + 9x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-18 + 9x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-6, 1.5}

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