(3+7x)(6+2x)=0

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Solution for (3+7x)(6+2x)=0 equation:


Simplifying
(3 + 7x)(6 + 2x) = 0

Multiply (3 + 7x) * (6 + 2x)
(3(6 + 2x) + 7x * (6 + 2x)) = 0
((6 * 3 + 2x * 3) + 7x * (6 + 2x)) = 0
((18 + 6x) + 7x * (6 + 2x)) = 0
(18 + 6x + (6 * 7x + 2x * 7x)) = 0
(18 + 6x + (42x + 14x2)) = 0

Combine like terms: 6x + 42x = 48x
(18 + 48x + 14x2) = 0

Solving
18 + 48x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 24x + 7x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(3 + 7x)' equal to zero and attempt to solve: Simplifying 3 + 7x = 0 Solving 3 + 7x = 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 + 7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x = 0 + -3 7x = 0 + -3 Combine like terms: 0 + -3 = -3 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286

Solution

x = {-3, -0.4285714286}

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