(2x-5)*(6+x)=2x-7x+12

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Solution for (2x-5)*(6+x)=2x-7x+12 equation:


Simplifying
(2x + -5)(6 + x) = 2x + -7x + 12

Reorder the terms:
(-5 + 2x)(6 + x) = 2x + -7x + 12

Multiply (-5 + 2x) * (6 + x)
(-5(6 + x) + 2x * (6 + x)) = 2x + -7x + 12
((6 * -5 + x * -5) + 2x * (6 + x)) = 2x + -7x + 12
((-30 + -5x) + 2x * (6 + x)) = 2x + -7x + 12
(-30 + -5x + (6 * 2x + x * 2x)) = 2x + -7x + 12
(-30 + -5x + (12x + 2x2)) = 2x + -7x + 12

Combine like terms: -5x + 12x = 7x
(-30 + 7x + 2x2) = 2x + -7x + 12

Reorder the terms:
-30 + 7x + 2x2 = 12 + 2x + -7x

Combine like terms: 2x + -7x = -5x
-30 + 7x + 2x2 = 12 + -5x

Solving
-30 + 7x + 2x2 = 12 + -5x

Solving for variable 'x'.

Reorder the terms:
-30 + -12 + 7x + 5x + 2x2 = 12 + -5x + -12 + 5x

Combine like terms: -30 + -12 = -42
-42 + 7x + 5x + 2x2 = 12 + -5x + -12 + 5x

Combine like terms: 7x + 5x = 12x
-42 + 12x + 2x2 = 12 + -5x + -12 + 5x

Reorder the terms:
-42 + 12x + 2x2 = 12 + -12 + -5x + 5x

Combine like terms: 12 + -12 = 0
-42 + 12x + 2x2 = 0 + -5x + 5x
-42 + 12x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-42 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-21 + 6x + x2)' equal to zero and attempt to solve: Simplifying -21 + 6x + x2 = 0 Solving -21 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 6x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 6x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 6x + x2 = 0 + 21 6x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 6x + x2 = 21 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 = 21 + 9 Reorder the terms: 9 + 6x + x2 = 21 + 9 Combine like terms: 21 + 9 = 30 9 + 6x + x2 = 30 Factor a perfect square on the left side: (x + 3)(x + 3) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 3) equal to 5.477225575 and -5.477225575.

Subproblem 1

x + 3 = 5.477225575 Simplifying x + 3 = 5.477225575 Reorder the terms: 3 + x = 5.477225575 Solving 3 + x = 5.477225575 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 = 5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.477225575 + -3 x = 5.477225575 + -3 Combine like terms: 5.477225575 + -3 = 2.477225575 x = 2.477225575 Simplifying x = 2.477225575

Subproblem 2

x + 3 = -5.477225575 Simplifying x + 3 = -5.477225575 Reorder the terms: 3 + x = -5.477225575 Solving 3 + x = -5.477225575 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 = -5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.477225575 + -3 x = -5.477225575 + -3 Combine like terms: -5.477225575 + -3 = -8.477225575 x = -8.477225575 Simplifying x = -8.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.477225575, -8.477225575}

Solution

x = {2.477225575, -8.477225575}

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