x^2+2x-3=9x+27

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Solution for x^2+2x-3=9x+27 equation:


Simplifying
x2 + 2x + -3 = 9x + 27

Reorder the terms:
-3 + 2x + x2 = 9x + 27

Reorder the terms:
-3 + 2x + x2 = 27 + 9x

Solving
-3 + 2x + x2 = 27 + 9x

Solving for variable 'x'.

Reorder the terms:
-3 + -27 + 2x + -9x + x2 = 27 + 9x + -27 + -9x

Combine like terms: -3 + -27 = -30
-30 + 2x + -9x + x2 = 27 + 9x + -27 + -9x

Combine like terms: 2x + -9x = -7x
-30 + -7x + x2 = 27 + 9x + -27 + -9x

Reorder the terms:
-30 + -7x + x2 = 27 + -27 + 9x + -9x

Combine like terms: 27 + -27 = 0
-30 + -7x + x2 = 0 + 9x + -9x
-30 + -7x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-30 + -7x + x2 = 0

Factor a trinomial.
(-3 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-3, 10}

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