4x(8-3x)-4=-2x(2+3x)+8

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Solution for 4x(8-3x)-4=-2x(2+3x)+8 equation:


Simplifying
4x(8 + -3x) + -4 = -2x(2 + 3x) + 8
(8 * 4x + -3x * 4x) + -4 = -2x(2 + 3x) + 8
(32x + -12x2) + -4 = -2x(2 + 3x) + 8

Reorder the terms:
-4 + 32x + -12x2 = -2x(2 + 3x) + 8
-4 + 32x + -12x2 = (2 * -2x + 3x * -2x) + 8
-4 + 32x + -12x2 = (-4x + -6x2) + 8

Reorder the terms:
-4 + 32x + -12x2 = 8 + -4x + -6x2

Solving
-4 + 32x + -12x2 = 8 + -4x + -6x2

Solving for variable 'x'.

Reorder the terms:
-4 + -8 + 32x + 4x + -12x2 + 6x2 = 8 + -4x + -6x2 + -8 + 4x + 6x2

Combine like terms: -4 + -8 = -12
-12 + 32x + 4x + -12x2 + 6x2 = 8 + -4x + -6x2 + -8 + 4x + 6x2

Combine like terms: 32x + 4x = 36x
-12 + 36x + -12x2 + 6x2 = 8 + -4x + -6x2 + -8 + 4x + 6x2

Combine like terms: -12x2 + 6x2 = -6x2
-12 + 36x + -6x2 = 8 + -4x + -6x2 + -8 + 4x + 6x2

Reorder the terms:
-12 + 36x + -6x2 = 8 + -8 + -4x + 4x + -6x2 + 6x2

Combine like terms: 8 + -8 = 0
-12 + 36x + -6x2 = 0 + -4x + 4x + -6x2 + 6x2
-12 + 36x + -6x2 = -4x + 4x + -6x2 + 6x2

Combine like terms: -4x + 4x = 0
-12 + 36x + -6x2 = 0 + -6x2 + 6x2
-12 + 36x + -6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-12 + 36x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 6x + -1x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-2 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + -1x2 = 0 Solving -2 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -6x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x + x2 = 0 + -2 -6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x + x2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6x + x2 = 7 Factor a perfect square on the left side: (x + -3)(x + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311

Subproblem 2

x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}

Solution

x = {5.645751311, 0.354248689}

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