(4x+6)*(2x+3)=0

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Solution for (4x+6)*(2x+3)=0 equation:


Simplifying
(4x + 6)(2x + 3) = 0

Reorder the terms:
(6 + 4x)(2x + 3) = 0

Reorder the terms:
(6 + 4x)(3 + 2x) = 0

Multiply (6 + 4x) * (3 + 2x)
(6(3 + 2x) + 4x * (3 + 2x)) = 0
((3 * 6 + 2x * 6) + 4x * (3 + 2x)) = 0
((18 + 12x) + 4x * (3 + 2x)) = 0
(18 + 12x + (3 * 4x + 2x * 4x)) = 0
(18 + 12x + (12x + 8x2)) = 0

Combine like terms: 12x + 12x = 24x
(18 + 24x + 8x2) = 0

Solving
18 + 24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 12x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {-1.5, -1.5}

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