(5x-3)(6+x)=0

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Solution for (5x-3)(6+x)=0 equation:


Simplifying
(5x + -3)(6 + x) = 0

Reorder the terms:
(-3 + 5x)(6 + x) = 0

Multiply (-3 + 5x) * (6 + x)
(-3(6 + x) + 5x * (6 + x)) = 0
((6 * -3 + x * -3) + 5x * (6 + x)) = 0
((-18 + -3x) + 5x * (6 + x)) = 0
(-18 + -3x + (6 * 5x + x * 5x)) = 0
(-18 + -3x + (30x + 5x2)) = 0

Combine like terms: -3x + 30x = 27x
(-18 + 27x + 5x2) = 0

Solving
-18 + 27x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(3 + -5x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Solution

x = {-6, 0.6}

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