(3x+7)(x-6)=0

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Solution for (3x+7)(x-6)=0 equation:


Simplifying
(3x + 7)(x + -6) = 0

Reorder the terms:
(7 + 3x)(x + -6) = 0

Reorder the terms:
(7 + 3x)(-6 + x) = 0

Multiply (7 + 3x) * (-6 + x)
(7(-6 + x) + 3x * (-6 + x)) = 0
((-6 * 7 + x * 7) + 3x * (-6 + x)) = 0
((-42 + 7x) + 3x * (-6 + x)) = 0
(-42 + 7x + (-6 * 3x + x * 3x)) = 0
(-42 + 7x + (-18x + 3x2)) = 0

Combine like terms: 7x + -18x = -11x
(-42 + -11x + 3x2) = 0

Solving
-42 + -11x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -3x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333

Subproblem 2

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

Solution

x = {-2.333333333, 6}

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