(x+7)(2x+3)=0

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Solution for (x+7)(2x+3)=0 equation:


Simplifying
(x + 7)(2x + 3) = 0

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

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

Multiply (7 + x) * (3 + 2x)
(7(3 + 2x) + x(3 + 2x)) = 0
((3 * 7 + 2x * 7) + x(3 + 2x)) = 0
((21 + 14x) + x(3 + 2x)) = 0
(21 + 14x + (3 * x + 2x * x)) = 0
(21 + 14x + (3x + 2x2)) = 0

Combine like terms: 14x + 3x = 17x
(21 + 17x + 2x2) = 0

Solving
21 + 17x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

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 = {-7, -1.5}

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