(x-4)(x+1)-(x+7)(x-3)=-7x+17

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Solution for (x-4)(x+1)-(x+7)(x-3)=-7x+17 equation: 


Simplifying
(x + -4)(x + 1) + -1(x + 7)(x + -3) = -7x + 17

Reorder the terms:
(-4 + x)(x + 1) + -1(x + 7)(x + -3) = -7x + 17

Reorder the terms:
(-4 + x)(1 + x) + -1(x + 7)(x + -3) = -7x + 17

Multiply (-4 + x) * (1 + x)
(-4(1 + x) + x(1 + x)) + -1(x + 7)(x + -3) = -7x + 17
((1 * -4 + x * -4) + x(1 + x)) + -1(x + 7)(x + -3) = -7x + 17
((-4 + -4x) + x(1 + x)) + -1(x + 7)(x + -3) = -7x + 17
(-4 + -4x + (1 * x + x * x)) + -1(x + 7)(x + -3) = -7x + 17
(-4 + -4x + (1x + x2)) + -1(x + 7)(x + -3) = -7x + 17

Combine like terms: -4x + 1x = -3x
(-4 + -3x + x2) + -1(x + 7)(x + -3) = -7x + 17

Reorder the terms:
-4 + -3x + x2 + -1(7 + x)(x + -3) = -7x + 17

Reorder the terms:
-4 + -3x + x2 + -1(7 + x)(-3 + x) = -7x + 17

Multiply (7 + x) * (-3 + x)
-4 + -3x + x2 + -1(7(-3 + x) + x(-3 + x)) = -7x + 17
-4 + -3x + x2 + -1((-3 * 7 + x * 7) + x(-3 + x)) = -7x + 17
-4 + -3x + x2 + -1((-21 + 7x) + x(-3 + x)) = -7x + 17
-4 + -3x + x2 + -1(-21 + 7x + (-3 * x + x * x)) = -7x + 17
-4 + -3x + x2 + -1(-21 + 7x + (-3x + x2)) = -7x + 17

Combine like terms: 7x + -3x = 4x
-4 + -3x + x2 + -1(-21 + 4x + x2) = -7x + 17
-4 + -3x + x2 + (-21 * -1 + 4x * -1 + x2 * -1) = -7x + 17
-4 + -3x + x2 + (21 + -4x + -1x2) = -7x + 17

Reorder the terms:
-4 + 21 + -3x + -4x + x2 + -1x2 = -7x + 17

Combine like terms: -4 + 21 = 17
17 + -3x + -4x + x2 + -1x2 = -7x + 17

Combine like terms: -3x + -4x = -7x
17 + -7x + x2 + -1x2 = -7x + 17

Combine like terms: x2 + -1x2 = 0
17 + -7x + 0 = -7x + 17
17 + -7x = -7x + 17

Reorder the terms:
17 + -7x = 17 + -7x

Add '-17' to each side of the equation.
17 + -17 + -7x = 17 + -17 + -7x

Combine like terms: 17 + -17 = 0
0 + -7x = 17 + -17 + -7x
-7x = 17 + -17 + -7x

Combine like terms: 17 + -17 = 0
-7x = 0 + -7x
-7x = -7x

Add '7x' to each side of the equation.
-7x + 7x = -7x + 7x

Combine like terms: -7x + 7x = 0
0 = -7x + 7x

Combine like terms: -7x + 7x = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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