2x(4x+12)+4x=-12

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Solution for 2x(4x+12)+4x=-12 equation:


Simplifying
2x(4x + 12) + 4x = -12

Reorder the terms:
2x(12 + 4x) + 4x = -12
(12 * 2x + 4x * 2x) + 4x = -12
(24x + 8x2) + 4x = -12

Reorder the terms:
24x + 4x + 8x2 = -12

Combine like terms: 24x + 4x = 28x
28x + 8x2 = -12

Solving
28x + 8x2 = -12

Solving for variable 'x'.

Reorder the terms:
12 + 28x + 8x2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 28x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 7x + 2x2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

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 = {-3, -0.5}

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