2x^2+3x=2(9-x)

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Solution for 2x^2+3x=2(9-x) equation:


Simplifying
2x2 + 3x = 2(9 + -1x)

Reorder the terms:
3x + 2x2 = 2(9 + -1x)
3x + 2x2 = (9 * 2 + -1x * 2)
3x + 2x2 = (18 + -2x)

Solving
3x + 2x2 = 18 + -2x

Solving for variable 'x'.

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

Combine like terms: 3x + 2x = 5x
-18 + 5x + 2x2 = 18 + -2x + -18 + 2x

Reorder the terms:
-18 + 5x + 2x2 = 18 + -18 + -2x + 2x

Combine like terms: 18 + -18 = 0
-18 + 5x + 2x2 = 0 + -2x + 2x
-18 + 5x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 5x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5

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 = {-4.5, 2}

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