(x^2+6x-8)(-4x)=

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Solution for (x^2+6x-8)(-4x)= equation:


Simplifying
(x2 + 6x + -8)(-4x) = 0

Reorder the terms:
(-8 + 6x + x2)(-4x) = 0

Remove parenthesis around (-4x)
(-8 + 6x + x2) * -4x = 0

Reorder the terms for easier multiplication:
-4x(-8 + 6x + x2) = 0
(-8 * -4x + 6x * -4x + x2 * -4x) = 0
(32x + -24x2 + -4x3) = 0

Solving
32x + -24x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(8 + -6x + -1x2) = 0

Ignore the factor 4.

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 '(8 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -6x + -1x2 = 0 Solving 8 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 6x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6x + x2 = 0 + 8 6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 6x + x2 = 8 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 8 + 9 Reorder the terms: 9 + 6x + x2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6x + x2 = 17 Factor a perfect square on the left side: (x + 3)(x + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 3) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + 3 = 4.123105626 Simplifying x + 3 = 4.123105626 Reorder the terms: 3 + x = 4.123105626 Solving 3 + x = 4.123105626 Solving for variable 'x'. 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.123105626 + -3 x = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 x = 1.123105626 Simplifying x = 1.123105626

Subproblem 2

x + 3 = -4.123105626 Simplifying x + 3 = -4.123105626 Reorder the terms: 3 + x = -4.123105626 Solving 3 + x = -4.123105626 Solving for variable 'x'. 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.123105626 + -3 x = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 x = -7.123105626 Simplifying x = -7.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.123105626, -7.123105626}

Solution

x = {0, 1.123105626, -7.123105626}

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