4(x+6)-x(x+6)=0

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Solution for 4(x+6)-x(x+6)=0 equation:


Simplifying
4(x + 6) + -1x(x + 6) = 0

Reorder the terms:
4(6 + x) + -1x(x + 6) = 0
(6 * 4 + x * 4) + -1x(x + 6) = 0
(24 + 4x) + -1x(x + 6) = 0

Reorder the terms:
24 + 4x + -1x(6 + x) = 0
24 + 4x + (6 * -1x + x * -1x) = 0
24 + 4x + (-6x + -1x2) = 0

Combine like terms: 4x + -6x = -2x
24 + -2x + -1x2 = 0

Solving
24 + -2x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(6 + x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

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

Solution

x = {4, -6}

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