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

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


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

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

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

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

Combine like terms: 12x + 8x = 20x
(12 + 20x + 8x2) = 0

Solving
12 + 20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 5x + 2x2) = 0

Factor a trinomial.
4((3 + 2x)(1 + x)) = 0

Ignore the factor 4.

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

Solution

x = {-1.5, -1}

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