(2x+9)(4x-3)=8x-12

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Solution for (2x+9)(4x-3)=8x-12 equation:


Simplifying
(2x + 9)(4x + -3) = 8x + -12

Reorder the terms:
(9 + 2x)(4x + -3) = 8x + -12

Reorder the terms:
(9 + 2x)(-3 + 4x) = 8x + -12

Multiply (9 + 2x) * (-3 + 4x)
(9(-3 + 4x) + 2x * (-3 + 4x)) = 8x + -12
((-3 * 9 + 4x * 9) + 2x * (-3 + 4x)) = 8x + -12
((-27 + 36x) + 2x * (-3 + 4x)) = 8x + -12
(-27 + 36x + (-3 * 2x + 4x * 2x)) = 8x + -12
(-27 + 36x + (-6x + 8x2)) = 8x + -12

Combine like terms: 36x + -6x = 30x
(-27 + 30x + 8x2) = 8x + -12

Reorder the terms:
-27 + 30x + 8x2 = -12 + 8x

Solving
-27 + 30x + 8x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
-27 + 12 + 30x + -8x + 8x2 = -12 + 8x + 12 + -8x

Combine like terms: -27 + 12 = -15
-15 + 30x + -8x + 8x2 = -12 + 8x + 12 + -8x

Combine like terms: 30x + -8x = 22x
-15 + 22x + 8x2 = -12 + 8x + 12 + -8x

Reorder the terms:
-15 + 22x + 8x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
-15 + 22x + 8x2 = 0 + 8x + -8x
-15 + 22x + 8x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + 22x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-1.875 + 2.75x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 2.75x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 2.75x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 2.75x + x2 = 0 + 1.875
2.75x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
2.75x + x2 = 1.875

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = 1.875 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 1.875 + 1.890625

Combine like terms: 1.875 + 1.890625 = 3.765625
1.890625 + 2.75x + x2 = 3.765625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + 1.375) equal to 1.940521837 and -1.940521837.

Subproblem 1

x + 1.375 = 1.940521837 Simplifying x + 1.375 = 1.940521837 Reorder the terms: 1.375 + x = 1.940521837 Solving 1.375 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.940521837 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.940521837 + -1.375 x = 1.940521837 + -1.375 Combine like terms: 1.940521837 + -1.375 = 0.565521837 x = 0.565521837 Simplifying x = 0.565521837

Subproblem 2

x + 1.375 = -1.940521837 Simplifying x + 1.375 = -1.940521837 Reorder the terms: 1.375 + x = -1.940521837 Solving 1.375 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.940521837 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.940521837 + -1.375 x = -1.940521837 + -1.375 Combine like terms: -1.940521837 + -1.375 = -3.315521837 x = -3.315521837 Simplifying x = -3.315521837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.565521837, -3.315521837}

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