7x^2-24=6x^2-5x

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Solution for 7x^2-24=6x^2-5x equation:


Simplifying
7x2 + -24 = 6x2 + -5x

Reorder the terms:
-24 + 7x2 = 6x2 + -5x

Reorder the terms:
-24 + 7x2 = -5x + 6x2

Solving
-24 + 7x2 = -5x + 6x2

Solving for variable 'x'.

Reorder the terms:
-24 + 5x + 7x2 + -6x2 = -5x + 6x2 + 5x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
-24 + 5x + 1x2 = -5x + 6x2 + 5x + -6x2

Reorder the terms:
-24 + 5x + 1x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
-24 + 5x + 1x2 = 0 + 6x2 + -6x2
-24 + 5x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-24 + 5x + 1x2 = 0

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

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 '(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

Solution

x = {-8, 3}

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