(x+5)(x-7)-(x-4)(x+3)=1

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Solution for (x+5)(x-7)-(x-4)(x+3)=1 equation: 


Simplifying
(x + 5)(x + -7) + -1(x + -4)(x + 3) = 1

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

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

Multiply (5 + x) * (-7 + x)
(5(-7 + x) + x(-7 + x)) + -1(x + -4)(x + 3) = 1
((-7 * 5 + x * 5) + x(-7 + x)) + -1(x + -4)(x + 3) = 1
((-35 + 5x) + x(-7 + x)) + -1(x + -4)(x + 3) = 1
(-35 + 5x + (-7 * x + x * x)) + -1(x + -4)(x + 3) = 1
(-35 + 5x + (-7x + x2)) + -1(x + -4)(x + 3) = 1

Combine like terms: 5x + -7x = -2x
(-35 + -2x + x2) + -1(x + -4)(x + 3) = 1

Reorder the terms:
-35 + -2x + x2 + -1(-4 + x)(x + 3) = 1

Reorder the terms:
-35 + -2x + x2 + -1(-4 + x)(3 + x) = 1

Multiply (-4 + x) * (3 + x)
-35 + -2x + x2 + -1(-4(3 + x) + x(3 + x)) = 1
-35 + -2x + x2 + -1((3 * -4 + x * -4) + x(3 + x)) = 1
-35 + -2x + x2 + -1((-12 + -4x) + x(3 + x)) = 1
-35 + -2x + x2 + -1(-12 + -4x + (3 * x + x * x)) = 1
-35 + -2x + x2 + -1(-12 + -4x + (3x + x2)) = 1

Combine like terms: -4x + 3x = -1x
-35 + -2x + x2 + -1(-12 + -1x + x2) = 1
-35 + -2x + x2 + (-12 * -1 + -1x * -1 + x2 * -1) = 1
-35 + -2x + x2 + (12 + 1x + -1x2) = 1

Reorder the terms:
-35 + 12 + -2x + 1x + x2 + -1x2 = 1

Combine like terms: -35 + 12 = -23
-23 + -2x + 1x + x2 + -1x2 = 1

Combine like terms: -2x + 1x = -1x
-23 + -1x + x2 + -1x2 = 1

Combine like terms: x2 + -1x2 = 0
-23 + -1x + 0 = 1
-23 + -1x = 1

Solving
-23 + -1x = 1

Solving for variable 'x'.

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 1 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 1 + 23
-1x = 1 + 23

Combine like terms: 1 + 23 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

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