(x+2)(2x+3)=6

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Solution for (x+2)(2x+3)=6 equation:


Simplifying
(x + 2)(2x + 3) = 6

Reorder the terms:
(2 + x)(2x + 3) = 6

Reorder the terms:
(2 + x)(3 + 2x) = 6

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = 6
((3 * 2 + 2x * 2) + x(3 + 2x)) = 6
((6 + 4x) + x(3 + 2x)) = 6
(6 + 4x + (3 * x + 2x * x)) = 6
(6 + 4x + (3x + 2x2)) = 6

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = 6

Add '-6' to each side of the equation.
6 + 7x + -6 + 2x2 = 6 + -6

Reorder the terms:
6 + -6 + 7x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + 7x + 2x2 = 6 + -6
7x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
7x + 2x2 = 0

Solving
7x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 2x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5

Solution

x = {0, -3.5}

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