(3x+4)(x^2+px+5)=-23x^2

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Solution for (3x+4)(x^2+px+5)=-23x^2 equation: 


Simplifying
(3x + 4)(x2 + px + 5) = -23x2

Reorder the terms:
(4 + 3x)(x2 + px + 5) = -23x2

Reorder the terms:
(4 + 3x)(5 + px + x2) = -23x2

Multiply (4 + 3x) * (5 + px + x2)
(4(5 + px + x2) + 3x * (5 + px + x2)) = -23x2
((5 * 4 + px * 4 + x2 * 4) + 3x * (5 + px + x2)) = -23x2
((20 + 4px + 4x2) + 3x * (5 + px + x2)) = -23x2
(20 + 4px + 4x2 + (5 * 3x + px * 3x + x2 * 3x)) = -23x2

Reorder the terms:
(20 + 4px + 4x2 + (3px2 + 15x + 3x3)) = -23x2
(20 + 4px + 4x2 + (3px2 + 15x + 3x3)) = -23x2

Reorder the terms:
(20 + 4px + 3px2 + 15x + 4x2 + 3x3) = -23x2
(20 + 4px + 3px2 + 15x + 4x2 + 3x3) = -23x2

Solving
20 + 4px + 3px2 + 15x + 4x2 + 3x3 = -23x2

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-20' to each side of the equation.
20 + 4px + 3px2 + 15x + 4x2 + -20 + 3x3 = -20 + -23x2

Reorder the terms:
20 + -20 + 4px + 3px2 + 15x + 4x2 + 3x3 = -20 + -23x2

Combine like terms: 20 + -20 = 0
0 + 4px + 3px2 + 15x + 4x2 + 3x3 = -20 + -23x2
4px + 3px2 + 15x + 4x2 + 3x3 = -20 + -23x2

Add '-15x' to each side of the equation.
4px + 3px2 + 15x + 4x2 + -15x + 3x3 = -20 + -15x + -23x2

Reorder the terms:
4px + 3px2 + 15x + -15x + 4x2 + 3x3 = -20 + -15x + -23x2

Combine like terms: 15x + -15x = 0
4px + 3px2 + 0 + 4x2 + 3x3 = -20 + -15x + -23x2
4px + 3px2 + 4x2 + 3x3 = -20 + -15x + -23x2

Add '-4x2' to each side of the equation.
4px + 3px2 + 4x2 + -4x2 + 3x3 = -20 + -15x + -23x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
4px + 3px2 + 0 + 3x3 = -20 + -15x + -23x2 + -4x2
4px + 3px2 + 3x3 = -20 + -15x + -23x2 + -4x2

Combine like terms: -23x2 + -4x2 = -27x2
4px + 3px2 + 3x3 = -20 + -15x + -27x2

Add '-3x3' to each side of the equation.
4px + 3px2 + 3x3 + -3x3 = -20 + -15x + -27x2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
4px + 3px2 + 0 = -20 + -15x + -27x2 + -3x3
4px + 3px2 = -20 + -15x + -27x2 + -3x3

Reorder the terms:
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = -20 + -15x + -27x2 + -3x3 + 20 + 15x + 27x2 + 3x3

Reorder the terms:
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = -20 + 20 + -15x + 15x + -27x2 + 27x2 + -3x3 + 3x3

Combine like terms: -20 + 20 = 0
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = 0 + -15x + 15x + -27x2 + 27x2 + -3x3 + 3x3
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = -15x + 15x + -27x2 + 27x2 + -3x3 + 3x3

Combine like terms: -15x + 15x = 0
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = 0 + -27x2 + 27x2 + -3x3 + 3x3
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = -27x2 + 27x2 + -3x3 + 3x3

Combine like terms: -27x2 + 27x2 = 0
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = 0 + -3x3 + 3x3
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
20 + 4px + 3px2 + 15x + 27x2 + 3x3 = 0

The solution to this equation could not be determined.

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