4(2x^2+3x-9)-3(x^2-5x+2)=

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Solution for 4(2x^2+3x-9)-3(x^2-5x+2)= equation:


Simplifying
4(2x2 + 3x + -9) + -3(x2 + -5x + 2) = 0

Reorder the terms:
4(-9 + 3x + 2x2) + -3(x2 + -5x + 2) = 0
(-9 * 4 + 3x * 4 + 2x2 * 4) + -3(x2 + -5x + 2) = 0
(-36 + 12x + 8x2) + -3(x2 + -5x + 2) = 0

Reorder the terms:
-36 + 12x + 8x2 + -3(2 + -5x + x2) = 0
-36 + 12x + 8x2 + (2 * -3 + -5x * -3 + x2 * -3) = 0
-36 + 12x + 8x2 + (-6 + 15x + -3x2) = 0

Reorder the terms:
-36 + -6 + 12x + 15x + 8x2 + -3x2 = 0

Combine like terms: -36 + -6 = -42
-42 + 12x + 15x + 8x2 + -3x2 = 0

Combine like terms: 12x + 15x = 27x
-42 + 27x + 8x2 + -3x2 = 0

Combine like terms: 8x2 + -3x2 = 5x2
-42 + 27x + 5x2 = 0

Solving
-42 + 27x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-8.4 + 5.4x + x2 = 0

Move the constant term to the right:

Add '8.4' to each side of the equation.
-8.4 + 5.4x + 8.4 + x2 = 0 + 8.4

Reorder the terms:
-8.4 + 8.4 + 5.4x + x2 = 0 + 8.4

Combine like terms: -8.4 + 8.4 = 0.0
0.0 + 5.4x + x2 = 0 + 8.4
5.4x + x2 = 0 + 8.4

Combine like terms: 0 + 8.4 = 8.4
5.4x + x2 = 8.4

The x term is 5.4x.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4x + 7.29 + x2 = 8.4 + 7.29

Reorder the terms:
7.29 + 5.4x + x2 = 8.4 + 7.29

Combine like terms: 8.4 + 7.29 = 15.69
7.29 + 5.4x + x2 = 15.69

Factor a perfect square on the left side:
(x + 2.7)(x + 2.7) = 15.69

Calculate the square root of the right side: 3.961060464

Break this problem into two subproblems by setting 
(x + 2.7) equal to 3.961060464 and -3.961060464.

Subproblem 1

x + 2.7 = 3.961060464 Simplifying x + 2.7 = 3.961060464 Reorder the terms: 2.7 + x = 3.961060464 Solving 2.7 + x = 3.961060464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 3.961060464 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 3.961060464 + -2.7 x = 3.961060464 + -2.7 Combine like terms: 3.961060464 + -2.7 = 1.261060464 x = 1.261060464 Simplifying x = 1.261060464

Subproblem 2

x + 2.7 = -3.961060464 Simplifying x + 2.7 = -3.961060464 Reorder the terms: 2.7 + x = -3.961060464 Solving 2.7 + x = -3.961060464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -3.961060464 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -3.961060464 + -2.7 x = -3.961060464 + -2.7 Combine like terms: -3.961060464 + -2.7 = -6.661060464 x = -6.661060464 Simplifying x = -6.661060464

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.261060464, -6.661060464}

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