(4x+24)(7x+3)=0

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Solution for (4x+24)(7x+3)=0 equation:


Simplifying
(4x + 24)(7x + 3) = 0

Reorder the terms:
(24 + 4x)(7x + 3) = 0

Reorder the terms:
(24 + 4x)(3 + 7x) = 0

Multiply (24 + 4x) * (3 + 7x)
(24(3 + 7x) + 4x * (3 + 7x)) = 0
((3 * 24 + 7x * 24) + 4x * (3 + 7x)) = 0
((72 + 168x) + 4x * (3 + 7x)) = 0
(72 + 168x + (3 * 4x + 7x * 4x)) = 0
(72 + 168x + (12x + 28x2)) = 0

Combine like terms: 168x + 12x = 180x
(72 + 180x + 28x2) = 0

Solving
72 + 180x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + 45x + 7x2) = 0

Factor a trinomial.
4((6 + x)(3 + 7x)) = 0

Ignore the factor 4.

Subproblem 1

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

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 = {-6, -0.4285714286}

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