(2x+3)(4x-2)=-6

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Solution for (2x+3)(4x-2)=-6 equation:


Simplifying
(2x + 3)(4x + -2) = -6

Reorder the terms:
(3 + 2x)(4x + -2) = -6

Reorder the terms:
(3 + 2x)(-2 + 4x) = -6

Multiply (3 + 2x) * (-2 + 4x)
(3(-2 + 4x) + 2x * (-2 + 4x)) = -6
((-2 * 3 + 4x * 3) + 2x * (-2 + 4x)) = -6
((-6 + 12x) + 2x * (-2 + 4x)) = -6
(-6 + 12x + (-2 * 2x + 4x * 2x)) = -6
(-6 + 12x + (-4x + 8x2)) = -6

Combine like terms: 12x + -4x = 8x
(-6 + 8x + 8x2) = -6

Add '6' to each side of the equation.
-6 + 8x + 6 + 8x2 = -6 + 6

Reorder the terms:
-6 + 6 + 8x + 8x2 = -6 + 6

Combine like terms: -6 + 6 = 0
0 + 8x + 8x2 = -6 + 6
8x + 8x2 = -6 + 6

Combine like terms: -6 + 6 = 0
8x + 8x2 = 0

Solving
8x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(1 + x) = 0

Ignore the factor 8.

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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0, -1}

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