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

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


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

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

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

Multiply (4 + x) * (-3 + x)
(4(-3 + x) + x(-3 + x)) = (x + 7)(x + -1)
((-3 * 4 + x * 4) + x(-3 + x)) = (x + 7)(x + -1)
((-12 + 4x) + x(-3 + x)) = (x + 7)(x + -1)
(-12 + 4x + (-3 * x + x * x)) = (x + 7)(x + -1)
(-12 + 4x + (-3x + x2)) = (x + 7)(x + -1)

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) = (x + 7)(x + -1)

Reorder the terms:
-12 + 1x + x2 = (7 + x)(x + -1)

Reorder the terms:
-12 + 1x + x2 = (7 + x)(-1 + x)

Multiply (7 + x) * (-1 + x)
-12 + 1x + x2 = (7(-1 + x) + x(-1 + x))
-12 + 1x + x2 = ((-1 * 7 + x * 7) + x(-1 + x))
-12 + 1x + x2 = ((-7 + 7x) + x(-1 + x))
-12 + 1x + x2 = (-7 + 7x + (-1 * x + x * x))
-12 + 1x + x2 = (-7 + 7x + (-1x + x2))

Combine like terms: 7x + -1x = 6x
-12 + 1x + x2 = (-7 + 6x + x2)

Add '-1x2' to each side of the equation.
-12 + 1x + x2 + -1x2 = -7 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x + 0 = -7 + 6x + x2 + -1x2
-12 + 1x = -7 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x = -7 + 6x + 0
-12 + 1x = -7 + 6x

Solving
-12 + 1x = -7 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
-12 + 1x + -6x = -7 + 6x + -6x

Combine like terms: 1x + -6x = -5x
-12 + -5x = -7 + 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + -5x = -7 + 0
-12 + -5x = -7

Add '12' to each side of the equation.
-12 + 12 + -5x = -7 + 12

Combine like terms: -12 + 12 = 0
0 + -5x = -7 + 12
-5x = -7 + 12

Combine like terms: -7 + 12 = 5
-5x = 5

Divide each side by '-5'.
x = -1

Simplifying
x = -1

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