4x+(x-5)(x+4)+15=(3-x)(x+3)+(x+6)(x-3)

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Solution for 4x+(x-5)(x+4)+15=(3-x)(x+3)+(x+6)(x-3) equation:


Simplifying
4x + (x + -5)(x + 4) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Reorder the terms:
4x + (-5 + x)(x + 4) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Reorder the terms:
4x + (-5 + x)(4 + x) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Multiply (-5 + x) * (4 + x)
4x + (-5(4 + x) + x(4 + x)) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)
4x + ((4 * -5 + x * -5) + x(4 + x)) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)
4x + ((-20 + -5x) + x(4 + x)) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)
4x + (-20 + -5x + (4 * x + x * x)) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)
4x + (-20 + -5x + (4x + x2)) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Combine like terms: -5x + 4x = -1x
4x + (-20 + -1x + x2) + 15 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Reorder the terms:
-20 + 15 + 4x + -1x + x2 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Combine like terms: -20 + 15 = -5
-5 + 4x + -1x + x2 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Combine like terms: 4x + -1x = 3x
-5 + 3x + x2 = (3 + -1x)(x + 3) + (x + 6)(x + -3)

Reorder the terms:
-5 + 3x + x2 = (3 + -1x)(3 + x) + (x + 6)(x + -3)

Multiply (3 + -1x) * (3 + x)
-5 + 3x + x2 = (3(3 + x) + -1x * (3 + x)) + (x + 6)(x + -3)
-5 + 3x + x2 = ((3 * 3 + x * 3) + -1x * (3 + x)) + (x + 6)(x + -3)
-5 + 3x + x2 = ((9 + 3x) + -1x * (3 + x)) + (x + 6)(x + -3)
-5 + 3x + x2 = (9 + 3x + (3 * -1x + x * -1x)) + (x + 6)(x + -3)
-5 + 3x + x2 = (9 + 3x + (-3x + -1x2)) + (x + 6)(x + -3)

Combine like terms: 3x + -3x = 0
-5 + 3x + x2 = (9 + 0 + -1x2) + (x + 6)(x + -3)
-5 + 3x + x2 = (9 + -1x2) + (x + 6)(x + -3)

Reorder the terms:
-5 + 3x + x2 = 9 + -1x2 + (6 + x)(x + -3)

Reorder the terms:
-5 + 3x + x2 = 9 + -1x2 + (6 + x)(-3 + x)

Multiply (6 + x) * (-3 + x)
-5 + 3x + x2 = 9 + -1x2 + (6(-3 + x) + x(-3 + x))
-5 + 3x + x2 = 9 + -1x2 + ((-3 * 6 + x * 6) + x(-3 + x))
-5 + 3x + x2 = 9 + -1x2 + ((-18 + 6x) + x(-3 + x))
-5 + 3x + x2 = 9 + -1x2 + (-18 + 6x + (-3 * x + x * x))
-5 + 3x + x2 = 9 + -1x2 + (-18 + 6x + (-3x + x2))

Combine like terms: 6x + -3x = 3x
-5 + 3x + x2 = 9 + -1x2 + (-18 + 3x + x2)

Reorder the terms:
-5 + 3x + x2 = 9 + -18 + 3x + -1x2 + x2

Combine like terms: 9 + -18 = -9
-5 + 3x + x2 = -9 + 3x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5 + 3x + x2 = -9 + 3x + 0
-5 + 3x + x2 = -9 + 3x

Add '-3x' to each side of the equation.
-5 + 3x + -3x + x2 = -9 + 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + 0 + x2 = -9 + 3x + -3x
-5 + x2 = -9 + 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + x2 = -9 + 0
-5 + x2 = -9

Solving
-5 + x2 = -9

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x2 = -9 + 5

Combine like terms: -5 + 5 = 0
0 + x2 = -9 + 5
x2 = -9 + 5

Combine like terms: -9 + 5 = -4
x2 = -4

Simplifying
x2 = -4

Reorder the terms:
4 + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + x2 = 0

The solution to this equation could not be determined.

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