(3x-3)(x+5)=3

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


Simplifying
(3x + -3)(x + 5) = 3

Reorder the terms:
(-3 + 3x)(x + 5) = 3

Reorder the terms:
(-3 + 3x)(5 + x) = 3

Multiply (-3 + 3x) * (5 + x)
(-3(5 + x) + 3x * (5 + x)) = 3
((5 * -3 + x * -3) + 3x * (5 + x)) = 3
((-15 + -3x) + 3x * (5 + x)) = 3
(-15 + -3x + (5 * 3x + x * 3x)) = 3
(-15 + -3x + (15x + 3x2)) = 3

Combine like terms: -3x + 15x = 12x
(-15 + 12x + 3x2) = 3

Solving
-15 + 12x + 3x2 = 3

Solving for variable 'x'.

Reorder the terms:
-15 + -3 + 12x + 3x2 = 3 + -3

Combine like terms: -15 + -3 = -18
-18 + 12x + 3x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-18 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-6 + 4x + x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + x2 = 0 Solving -6 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4x + x2 = 0 + 6 4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4x + x2 = 6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 6 + 4 Reorder the terms: 4 + 4x + x2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4x + x2 = 10 Factor a perfect square on the left side: (x + 2)(x + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 2 = 3.16227766 Simplifying x + 2 = 3.16227766 Reorder the terms: 2 + x = 3.16227766 Solving 2 + x = 3.16227766 Solving for variable 'x'. 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 = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.16227766 + -2 x = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 x = 1.16227766 Simplifying x = 1.16227766

Subproblem 2

x + 2 = -3.16227766 Simplifying x + 2 = -3.16227766 Reorder the terms: 2 + x = -3.16227766 Solving 2 + x = -3.16227766 Solving for variable 'x'. 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 = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.16227766 + -2 x = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 x = -5.16227766 Simplifying x = -5.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.16227766, -5.16227766}

Solution

x = {1.16227766, -5.16227766}

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