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

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


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

Reorder the terms:
2(3 + 4x) + 4 = 3x(2x + 4)
(3 * 2 + 4x * 2) + 4 = 3x(2x + 4)
(6 + 8x) + 4 = 3x(2x + 4)

Reorder the terms:
6 + 4 + 8x = 3x(2x + 4)

Combine like terms: 6 + 4 = 10
10 + 8x = 3x(2x + 4)

Reorder the terms:
10 + 8x = 3x(4 + 2x)
10 + 8x = (4 * 3x + 2x * 3x)
10 + 8x = (12x + 6x2)

Solving
10 + 8x = 12x + 6x2

Solving for variable 'x'.

Combine like terms: 8x + -12x = -4x
10 + -4x + -6x2 = 12x + 6x2 + -12x + -6x2

Reorder the terms:
10 + -4x + -6x2 = 12x + -12x + 6x2 + -6x2

Combine like terms: 12x + -12x = 0
10 + -4x + -6x2 = 0 + 6x2 + -6x2
10 + -4x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
10 + -4x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -2x + -3x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + 3x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667

Solution

x = {1, -1.666666667}

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