(4x+1)(2x+3)=

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Solution for (4x+1)(2x+3)= equation:


Simplifying
(4x + 1)(2x + 3) = 0

Reorder the terms:
(1 + 4x)(2x + 3) = 0

Reorder the terms:
(1 + 4x)(3 + 2x) = 0

Multiply (1 + 4x) * (3 + 2x)
(1(3 + 2x) + 4x * (3 + 2x)) = 0
((3 * 1 + 2x * 1) + 4x * (3 + 2x)) = 0
((3 + 2x) + 4x * (3 + 2x)) = 0
(3 + 2x + (3 * 4x + 2x * 4x)) = 0
(3 + 2x + (12x + 8x2)) = 0

Combine like terms: 2x + 12x = 14x
(3 + 14x + 8x2) = 0

Solving
3 + 14x + 8x2 = 0

Solving for variable 'x'.

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

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 + 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 = {-1.5, -0.25}

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