x^2-3x+27=8x+3

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Solution for x^2-3x+27=8x+3 equation:


Simplifying
x2 + -3x + 27 = 8x + 3

Reorder the terms:
27 + -3x + x2 = 8x + 3

Reorder the terms:
27 + -3x + x2 = 3 + 8x

Solving
27 + -3x + x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
27 + -3 + -3x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: 27 + -3 = 24
24 + -3x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: -3x + -8x = -11x
24 + -11x + x2 = 3 + 8x + -3 + -8x

Reorder the terms:
24 + -11x + x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
24 + -11x + x2 = 0 + 8x + -8x
24 + -11x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
24 + -11x + x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {3, 8}

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