(x+3)(2x+1)=7

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Solution for (x+3)(2x+1)=7 equation:


Simplifying
(x + 3)(2x + 1) = 7

Reorder the terms:
(3 + x)(2x + 1) = 7

Reorder the terms:
(3 + x)(1 + 2x) = 7

Multiply (3 + x) * (1 + 2x)
(3(1 + 2x) + x(1 + 2x)) = 7
((1 * 3 + 2x * 3) + x(1 + 2x)) = 7
((3 + 6x) + x(1 + 2x)) = 7
(3 + 6x + (1 * x + 2x * x)) = 7
(3 + 6x + (1x + 2x2)) = 7

Combine like terms: 6x + 1x = 7x
(3 + 7x + 2x2) = 7

Solving
3 + 7x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
3 + -7 + 7x + 2x2 = 7 + -7

Combine like terms: 3 + -7 = -4
-4 + 7x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-4 + 7x + 2x2 = 0

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

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-4, 0.5}

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