6x+54+9x=2x^2+18x

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Solution for 6x+54+9x=2x^2+18x equation:


Simplifying
6x + 54 + 9x = 2x2 + 18x

Reorder the terms:
54 + 6x + 9x = 2x2 + 18x

Combine like terms: 6x + 9x = 15x
54 + 15x = 2x2 + 18x

Reorder the terms:
54 + 15x = 18x + 2x2

Solving
54 + 15x = 18x + 2x2

Solving for variable 'x'.

Combine like terms: 15x + -18x = -3x
54 + -3x + -2x2 = 18x + 2x2 + -18x + -2x2

Reorder the terms:
54 + -3x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
54 + -3x + -2x2 = 0 + 2x2 + -2x2
54 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
54 + -3x + -2x2 = 0

Factor a trinomial.
(9 + -2x)(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {4.5, -6}

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