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

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


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

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

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

Multiply (-7 + x) * (6 + 3x)
(-7(6 + 3x) + x(6 + 3x)) = 0
((6 * -7 + 3x * -7) + x(6 + 3x)) = 0
((-42 + -21x) + x(6 + 3x)) = 0
(-42 + -21x + (6 * x + 3x * x)) = 0
(-42 + -21x + (6x + 3x2)) = 0

Combine like terms: -21x + 6x = -15x
(-42 + -15x + 3x2) = 0

Solving
-42 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -5x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(7 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-2, 7}

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