6x^2+9x-16=2x^2+5x+8

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Solution for 6x^2+9x-16=2x^2+5x+8 equation:


Simplifying
6x2 + 9x + -16 = 2x2 + 5x + 8

Reorder the terms:
-16 + 9x + 6x2 = 2x2 + 5x + 8

Reorder the terms:
-16 + 9x + 6x2 = 8 + 5x + 2x2

Solving
-16 + 9x + 6x2 = 8 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + -8 + 9x + -5x + 6x2 + -2x2 = 8 + 5x + 2x2 + -8 + -5x + -2x2

Combine like terms: -16 + -8 = -24
-24 + 9x + -5x + 6x2 + -2x2 = 8 + 5x + 2x2 + -8 + -5x + -2x2

Combine like terms: 9x + -5x = 4x
-24 + 4x + 6x2 + -2x2 = 8 + 5x + 2x2 + -8 + -5x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-24 + 4x + 4x2 = 8 + 5x + 2x2 + -8 + -5x + -2x2

Reorder the terms:
-24 + 4x + 4x2 = 8 + -8 + 5x + -5x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-24 + 4x + 4x2 = 0 + 5x + -5x + 2x2 + -2x2
-24 + 4x + 4x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-24 + 4x + 4x2 = 0 + 2x2 + -2x2
-24 + 4x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-24 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

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 '(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 = {-3, 2}

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