4x(x-3)-5(3x-6)=(2x-3)2

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Solution for 4x(x-3)-5(3x-6)=(2x-3)2 equation:


Simplifying
4x(x + -3) + -5(3x + -6) = (2x + -3) * 2

Reorder the terms:
4x(-3 + x) + -5(3x + -6) = (2x + -3) * 2
(-3 * 4x + x * 4x) + -5(3x + -6) = (2x + -3) * 2
(-12x + 4x2) + -5(3x + -6) = (2x + -3) * 2

Reorder the terms:
-12x + 4x2 + -5(-6 + 3x) = (2x + -3) * 2
-12x + 4x2 + (-6 * -5 + 3x * -5) = (2x + -3) * 2
-12x + 4x2 + (30 + -15x) = (2x + -3) * 2

Reorder the terms:
30 + -12x + -15x + 4x2 = (2x + -3) * 2

Combine like terms: -12x + -15x = -27x
30 + -27x + 4x2 = (2x + -3) * 2

Reorder the terms:
30 + -27x + 4x2 = (-3 + 2x) * 2

Reorder the terms for easier multiplication:
30 + -27x + 4x2 = 2(-3 + 2x)
30 + -27x + 4x2 = (-3 * 2 + 2x * 2)
30 + -27x + 4x2 = (-6 + 4x)

Solving
30 + -27x + 4x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
30 + 6 + -27x + -4x + 4x2 = -6 + 4x + 6 + -4x

Combine like terms: 30 + 6 = 36
36 + -27x + -4x + 4x2 = -6 + 4x + 6 + -4x

Combine like terms: -27x + -4x = -31x
36 + -31x + 4x2 = -6 + 4x + 6 + -4x

Reorder the terms:
36 + -31x + 4x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
36 + -31x + 4x2 = 0 + 4x + -4x
36 + -31x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
36 + -31x + 4x2 = 0

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

Divide each side by '4'.
9 + -7.75x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -7.75x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -7.75x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7.75x + x2 = 0 + -9
-7.75x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-7.75x + x2 = -9

The x term is -7.75x.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75x + 15.015625 + x2 = -9 + 15.015625

Reorder the terms:
15.015625 + -7.75x + x2 = -9 + 15.015625

Combine like terms: -9 + 15.015625 = 6.015625
15.015625 + -7.75x + x2 = 6.015625

Factor a perfect square on the left side:
(x + -3.875)(x + -3.875) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(x + -3.875) equal to 2.452677109 and -2.452677109.

Subproblem 1

x + -3.875 = 2.452677109 Simplifying x + -3.875 = 2.452677109 Reorder the terms: -3.875 + x = 2.452677109 Solving -3.875 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 2.452677109 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 2.452677109 + 3.875 x = 2.452677109 + 3.875 Combine like terms: 2.452677109 + 3.875 = 6.327677109 x = 6.327677109 Simplifying x = 6.327677109

Subproblem 2

x + -3.875 = -2.452677109 Simplifying x + -3.875 = -2.452677109 Reorder the terms: -3.875 + x = -2.452677109 Solving -3.875 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -2.452677109 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -2.452677109 + 3.875 x = -2.452677109 + 3.875 Combine like terms: -2.452677109 + 3.875 = 1.422322891 x = 1.422322891 Simplifying x = 1.422322891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.327677109, 1.422322891}

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