30=.5(3x+x)(x-2)

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Solution for 30=.5(3x+x)(x-2) equation:


Simplifying
30 = 0.5(3x + x)(x + -2)

Combine like terms: 3x + x = 4x
30 = 0.5(4x)(x + -2)

Remove parenthesis around (4x)
30 = 0.5 * 4x(x + -2)

Reorder the terms:
30 = 0.5 * 4x(-2 + x)

Multiply 0.5 * 4
30 = 2x(-2 + x)
30 = (-2 * 2x + x * 2x)
30 = (-4x + 2x2)

Solving
30 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
30 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
30 + 4x + -2x2 = 0 + 2x2 + -2x2
30 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 2x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

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

Solution

x = {5, -3}

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