24x^2+17x=6x^2-7x

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Solution for 24x^2+17x=6x^2-7x equation:


Simplifying
24x2 + 17x = 6x2 + -7x

Reorder the terms:
17x + 24x2 = 6x2 + -7x

Reorder the terms:
17x + 24x2 = -7x + 6x2

Solving
17x + 24x2 = -7x + 6x2

Solving for variable 'x'.

Reorder the terms:
17x + 7x + 24x2 + -6x2 = -7x + 6x2 + 7x + -6x2

Combine like terms: 17x + 7x = 24x
24x + 24x2 + -6x2 = -7x + 6x2 + 7x + -6x2

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

Reorder the terms:
24x + 18x2 = -7x + 7x + 6x2 + -6x2

Combine like terms: -7x + 7x = 0
24x + 18x2 = 0 + 6x2 + -6x2
24x + 18x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
24x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(4 + 3x) = 0

Ignore the factor 6.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333

Solution

x = {0, -1.333333333}

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