3x^2+2x+24=2x^2-7x+6

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Solution for 3x^2+2x+24=2x^2-7x+6 equation:


Simplifying
3x2 + 2x + 24 = 2x2 + -7x + 6

Reorder the terms:
24 + 2x + 3x2 = 2x2 + -7x + 6

Reorder the terms:
24 + 2x + 3x2 = 6 + -7x + 2x2

Solving
24 + 2x + 3x2 = 6 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
24 + -6 + 2x + 7x + 3x2 + -2x2 = 6 + -7x + 2x2 + -6 + 7x + -2x2

Combine like terms: 24 + -6 = 18
18 + 2x + 7x + 3x2 + -2x2 = 6 + -7x + 2x2 + -6 + 7x + -2x2

Combine like terms: 2x + 7x = 9x
18 + 9x + 3x2 + -2x2 = 6 + -7x + 2x2 + -6 + 7x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
18 + 9x + 1x2 = 6 + -7x + 2x2 + -6 + 7x + -2x2

Reorder the terms:
18 + 9x + 1x2 = 6 + -6 + -7x + 7x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
18 + 9x + 1x2 = 0 + -7x + 7x + 2x2 + -2x2
18 + 9x + 1x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
18 + 9x + 1x2 = 0 + 2x2 + -2x2
18 + 9x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + 9x + 1x2 = 0

Factor a trinomial.
(6 + x)(3 + x) = 0

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-6, -3}

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