(4x+2)(x+7)+(x-3)(4x+2)=0

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Solution for (4x+2)(x+7)+(x-3)(4x+2)=0 equation:


Simplifying
(4x + 2)(x + 7) + (x + -3)(4x + 2) = 0

Reorder the terms:
(2 + 4x)(x + 7) + (x + -3)(4x + 2) = 0

Reorder the terms:
(2 + 4x)(7 + x) + (x + -3)(4x + 2) = 0

Multiply (2 + 4x) * (7 + x)
(2(7 + x) + 4x * (7 + x)) + (x + -3)(4x + 2) = 0
((7 * 2 + x * 2) + 4x * (7 + x)) + (x + -3)(4x + 2) = 0
((14 + 2x) + 4x * (7 + x)) + (x + -3)(4x + 2) = 0
(14 + 2x + (7 * 4x + x * 4x)) + (x + -3)(4x + 2) = 0
(14 + 2x + (28x + 4x2)) + (x + -3)(4x + 2) = 0

Combine like terms: 2x + 28x = 30x
(14 + 30x + 4x2) + (x + -3)(4x + 2) = 0

Reorder the terms:
14 + 30x + 4x2 + (-3 + x)(4x + 2) = 0

Reorder the terms:
14 + 30x + 4x2 + (-3 + x)(2 + 4x) = 0

Multiply (-3 + x) * (2 + 4x)
14 + 30x + 4x2 + (-3(2 + 4x) + x(2 + 4x)) = 0
14 + 30x + 4x2 + ((2 * -3 + 4x * -3) + x(2 + 4x)) = 0
14 + 30x + 4x2 + ((-6 + -12x) + x(2 + 4x)) = 0
14 + 30x + 4x2 + (-6 + -12x + (2 * x + 4x * x)) = 0
14 + 30x + 4x2 + (-6 + -12x + (2x + 4x2)) = 0

Combine like terms: -12x + 2x = -10x
14 + 30x + 4x2 + (-6 + -10x + 4x2) = 0

Reorder the terms:
14 + -6 + 30x + -10x + 4x2 + 4x2 = 0

Combine like terms: 14 + -6 = 8
8 + 30x + -10x + 4x2 + 4x2 = 0

Combine like terms: 30x + -10x = 20x
8 + 20x + 4x2 + 4x2 = 0

Combine like terms: 4x2 + 4x2 = 8x2
8 + 20x + 8x2 = 0

Solving
8 + 20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 5x + 2x2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

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 = {-2, -0.5}

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