(2x+9)(x^2+7x+4)=4x(x^2+7x+4)+9(x^2+7x+4)

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Solution for (2x+9)(x^2+7x+4)=4x(x^2+7x+4)+9(x^2+7x+4) equation:


Simplifying
(2x + 9)(x2 + 7x + 4) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Reorder the terms:
(9 + 2x)(x2 + 7x + 4) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Reorder the terms:
(9 + 2x)(4 + 7x + x2) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Multiply (9 + 2x) * (4 + 7x + x2)
(9(4 + 7x + x2) + 2x * (4 + 7x + x2)) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)
((4 * 9 + 7x * 9 + x2 * 9) + 2x * (4 + 7x + x2)) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)
((36 + 63x + 9x2) + 2x * (4 + 7x + x2)) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)
(36 + 63x + 9x2 + (4 * 2x + 7x * 2x + x2 * 2x)) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)
(36 + 63x + 9x2 + (8x + 14x2 + 2x3)) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Reorder the terms:
(36 + 63x + 8x + 9x2 + 14x2 + 2x3) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Combine like terms: 63x + 8x = 71x
(36 + 71x + 9x2 + 14x2 + 2x3) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Combine like terms: 9x2 + 14x2 = 23x2
(36 + 71x + 23x2 + 2x3) = 4x(x2 + 7x + 4) + 9(x2 + 7x + 4)

Reorder the terms:
36 + 71x + 23x2 + 2x3 = 4x(4 + 7x + x2) + 9(x2 + 7x + 4)
36 + 71x + 23x2 + 2x3 = (4 * 4x + 7x * 4x + x2 * 4x) + 9(x2 + 7x + 4)
36 + 71x + 23x2 + 2x3 = (16x + 28x2 + 4x3) + 9(x2 + 7x + 4)

Reorder the terms:
36 + 71x + 23x2 + 2x3 = 16x + 28x2 + 4x3 + 9(4 + 7x + x2)
36 + 71x + 23x2 + 2x3 = 16x + 28x2 + 4x3 + (4 * 9 + 7x * 9 + x2 * 9)
36 + 71x + 23x2 + 2x3 = 16x + 28x2 + 4x3 + (36 + 63x + 9x2)

Reorder the terms:
36 + 71x + 23x2 + 2x3 = 36 + 16x + 63x + 28x2 + 9x2 + 4x3

Combine like terms: 16x + 63x = 79x
36 + 71x + 23x2 + 2x3 = 36 + 79x + 28x2 + 9x2 + 4x3

Combine like terms: 28x2 + 9x2 = 37x2
36 + 71x + 23x2 + 2x3 = 36 + 79x + 37x2 + 4x3

Add '-36' to each side of the equation.
36 + 71x + 23x2 + -36 + 2x3 = 36 + 79x + 37x2 + -36 + 4x3

Reorder the terms:
36 + -36 + 71x + 23x2 + 2x3 = 36 + 79x + 37x2 + -36 + 4x3

Combine like terms: 36 + -36 = 0
0 + 71x + 23x2 + 2x3 = 36 + 79x + 37x2 + -36 + 4x3
71x + 23x2 + 2x3 = 36 + 79x + 37x2 + -36 + 4x3

Reorder the terms:
71x + 23x2 + 2x3 = 36 + -36 + 79x + 37x2 + 4x3

Combine like terms: 36 + -36 = 0
71x + 23x2 + 2x3 = 0 + 79x + 37x2 + 4x3
71x + 23x2 + 2x3 = 79x + 37x2 + 4x3

Solving
71x + 23x2 + 2x3 = 79x + 37x2 + 4x3

Solving for variable 'x'.

Reorder the terms:
71x + -79x + 23x2 + -37x2 + 2x3 + -4x3 = 79x + 37x2 + 4x3 + -79x + -37x2 + -4x3

Combine like terms: 71x + -79x = -8x
-8x + 23x2 + -37x2 + 2x3 + -4x3 = 79x + 37x2 + 4x3 + -79x + -37x2 + -4x3

Combine like terms: 23x2 + -37x2 = -14x2
-8x + -14x2 + 2x3 + -4x3 = 79x + 37x2 + 4x3 + -79x + -37x2 + -4x3

Combine like terms: 2x3 + -4x3 = -2x3
-8x + -14x2 + -2x3 = 79x + 37x2 + 4x3 + -79x + -37x2 + -4x3

Reorder the terms:
-8x + -14x2 + -2x3 = 79x + -79x + 37x2 + -37x2 + 4x3 + -4x3

Combine like terms: 79x + -79x = 0
-8x + -14x2 + -2x3 = 0 + 37x2 + -37x2 + 4x3 + -4x3
-8x + -14x2 + -2x3 = 37x2 + -37x2 + 4x3 + -4x3

Combine like terms: 37x2 + -37x2 = 0
-8x + -14x2 + -2x3 = 0 + 4x3 + -4x3
-8x + -14x2 + -2x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-8x + -14x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(4 + 7x + x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(4 + 7x + x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + x2 = 0 Solving 4 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 7x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x + x2 = 0 + -4 7x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 7x + x2 = -4 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7x + x2 = 8.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 3.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + 3.5 = 2.872281323 Simplifying x + 3.5 = 2.872281323 Reorder the terms: 3.5 + x = 2.872281323 Solving 3.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.872281323 + -3.5 x = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 x = -0.627718677 Simplifying x = -0.627718677

Subproblem 2

x + 3.5 = -2.872281323 Simplifying x + 3.5 = -2.872281323 Reorder the terms: 3.5 + x = -2.872281323 Solving 3.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.872281323 + -3.5 x = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 x = -6.372281323 Simplifying x = -6.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.627718677, -6.372281323}

Solution

x = {0, -0.627718677, -6.372281323}

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