2x^2+21x-51=-x^2+3x-3

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Solution for 2x^2+21x-51=-x^2+3x-3 equation:


Simplifying
2x2 + 21x + -51 = -1x2 + 3x + -3

Reorder the terms:
-51 + 21x + 2x2 = -1x2 + 3x + -3

Reorder the terms:
-51 + 21x + 2x2 = -3 + 3x + -1x2

Solving
-51 + 21x + 2x2 = -3 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
-51 + 3 + 21x + -3x + 2x2 + x2 = -3 + 3x + -1x2 + 3 + -3x + x2

Combine like terms: -51 + 3 = -48
-48 + 21x + -3x + 2x2 + x2 = -3 + 3x + -1x2 + 3 + -3x + x2

Combine like terms: 21x + -3x = 18x
-48 + 18x + 2x2 + x2 = -3 + 3x + -1x2 + 3 + -3x + x2

Combine like terms: 2x2 + x2 = 3x2
-48 + 18x + 3x2 = -3 + 3x + -1x2 + 3 + -3x + x2

Reorder the terms:
-48 + 18x + 3x2 = -3 + 3 + 3x + -3x + -1x2 + x2

Combine like terms: -3 + 3 = 0
-48 + 18x + 3x2 = 0 + 3x + -3x + -1x2 + x2
-48 + 18x + 3x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-48 + 18x + 3x2 = 0 + -1x2 + x2
-48 + 18x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-48 + 18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 6x + x2) = 0

Factor a trinomial.
3((-8 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

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

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 = {-8, 2}

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