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

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


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

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

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

Multiply (-4 + x) * (7 + x)
(-4(7 + x) + x(7 + x)) = (x + 4)(x + -3)
((7 * -4 + x * -4) + x(7 + x)) = (x + 4)(x + -3)
((-28 + -4x) + x(7 + x)) = (x + 4)(x + -3)
(-28 + -4x + (7 * x + x * x)) = (x + 4)(x + -3)
(-28 + -4x + (7x + x2)) = (x + 4)(x + -3)

Combine like terms: -4x + 7x = 3x
(-28 + 3x + x2) = (x + 4)(x + -3)

Reorder the terms:
-28 + 3x + x2 = (4 + x)(x + -3)

Reorder the terms:
-28 + 3x + x2 = (4 + x)(-3 + x)

Multiply (4 + x) * (-3 + x)
-28 + 3x + x2 = (4(-3 + x) + x(-3 + x))
-28 + 3x + x2 = ((-3 * 4 + x * 4) + x(-3 + x))
-28 + 3x + x2 = ((-12 + 4x) + x(-3 + x))
-28 + 3x + x2 = (-12 + 4x + (-3 * x + x * x))
-28 + 3x + x2 = (-12 + 4x + (-3x + x2))

Combine like terms: 4x + -3x = 1x
-28 + 3x + x2 = (-12 + 1x + x2)

Add '-1x2' to each side of the equation.
-28 + 3x + x2 + -1x2 = -12 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + 3x + 0 = -12 + 1x + x2 + -1x2
-28 + 3x = -12 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + 3x = -12 + 1x + 0
-28 + 3x = -12 + 1x

Solving
-28 + 3x = -12 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-28 + 3x + -1x = -12 + 1x + -1x

Combine like terms: 3x + -1x = 2x
-28 + 2x = -12 + 1x + -1x

Combine like terms: 1x + -1x = 0
-28 + 2x = -12 + 0
-28 + 2x = -12

Add '28' to each side of the equation.
-28 + 28 + 2x = -12 + 28

Combine like terms: -28 + 28 = 0
0 + 2x = -12 + 28
2x = -12 + 28

Combine like terms: -12 + 28 = 16
2x = 16

Divide each side by '2'.
x = 8

Simplifying
x = 8

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