-3x+3x^2=45+3x

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Solution for -3x+3x^2=45+3x equation:


Simplifying
-3x + 3x2 = 45 + 3x

Solving
-3x + 3x2 = 45 + 3x

Solving for variable 'x'.

Reorder the terms:
-45 + -3x + -3x + 3x2 = 45 + 3x + -45 + -3x

Combine like terms: -3x + -3x = -6x
-45 + -6x + 3x2 = 45 + 3x + -45 + -3x

Reorder the terms:
-45 + -6x + 3x2 = 45 + -45 + 3x + -3x

Combine like terms: 45 + -45 = 0
-45 + -6x + 3x2 = 0 + 3x + -3x
-45 + -6x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-45 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-3, 5}

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