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

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


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

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

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

Multiply (-6 + 7x) * (6 + 3x)
(-6(6 + 3x) + 7x * (6 + 3x)) = 0
((6 * -6 + 3x * -6) + 7x * (6 + 3x)) = 0
((-36 + -18x) + 7x * (6 + 3x)) = 0
(-36 + -18x + (6 * 7x + 3x * 7x)) = 0
(-36 + -18x + (42x + 21x2)) = 0

Combine like terms: -18x + 42x = 24x
(-36 + 24x + 21x2) = 0

Solving
-36 + 24x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8x + 7x2) = 0

Factor a trinomial.
3((-2 + -1x)(6 + -7x)) = 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 '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 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 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571

Solution

x = {-2, 0.8571428571}

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