(4x+3)(4x+1)=0

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Solution for (4x+3)(4x+1)=0 equation:


Simplifying
(4x + 3)(4x + 1) = 0

Reorder the terms:
(3 + 4x)(4x + 1) = 0

Reorder the terms:
(3 + 4x)(1 + 4x) = 0

Multiply (3 + 4x) * (1 + 4x)
(3(1 + 4x) + 4x * (1 + 4x)) = 0
((1 * 3 + 4x * 3) + 4x * (1 + 4x)) = 0
((3 + 12x) + 4x * (1 + 4x)) = 0
(3 + 12x + (1 * 4x + 4x * 4x)) = 0
(3 + 12x + (4x + 16x2)) = 0

Combine like terms: 12x + 4x = 16x
(3 + 16x + 16x2) = 0

Solving
3 + 16x + 16x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75

Subproblem 2

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Solution

x = {-0.75, -0.25}

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