3x(x-2)+7x=24

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Solution for 3x(x-2)+7x=24 equation:


Simplifying
3x(x + -2) + 7x = 24

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

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

Combine like terms: -6x + 7x = 1x
1x + 3x2 = 24

Solving
1x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 1x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 1x + 3x2 = 0

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

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 '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 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 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667

Solution

x = {-3, 2.666666667}

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