(x+3)(x-4)=(2x+7)(x-4)

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Solution for (x+3)(x-4)=(2x+7)(x-4) equation: 


Simplifying
(x + 3)(x + -4) = (2x + 7)(x + -4)

Reorder the terms:
(3 + x)(x + -4) = (2x + 7)(x + -4)

Reorder the terms:
(3 + x)(-4 + x) = (2x + 7)(x + -4)

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = (2x + 7)(x + -4)
((-4 * 3 + x * 3) + x(-4 + x)) = (2x + 7)(x + -4)
((-12 + 3x) + x(-4 + x)) = (2x + 7)(x + -4)
(-12 + 3x + (-4 * x + x * x)) = (2x + 7)(x + -4)
(-12 + 3x + (-4x + x2)) = (2x + 7)(x + -4)

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = (2x + 7)(x + -4)

Reorder the terms:
-12 + -1x + x2 = (7 + 2x)(x + -4)

Reorder the terms:
-12 + -1x + x2 = (7 + 2x)(-4 + x)

Multiply (7 + 2x) * (-4 + x)
-12 + -1x + x2 = (7(-4 + x) + 2x * (-4 + x))
-12 + -1x + x2 = ((-4 * 7 + x * 7) + 2x * (-4 + x))
-12 + -1x + x2 = ((-28 + 7x) + 2x * (-4 + x))
-12 + -1x + x2 = (-28 + 7x + (-4 * 2x + x * 2x))
-12 + -1x + x2 = (-28 + 7x + (-8x + 2x2))

Combine like terms: 7x + -8x = -1x
-12 + -1x + x2 = (-28 + -1x + 2x2)

Add 'x' to each side of the equation.
-12 + -1x + x + x2 = -28 + -1x + x + 2x2

Combine like terms: -1x + x = 0
-12 + 0 + x2 = -28 + -1x + x + 2x2
-12 + x2 = -28 + -1x + x + 2x2

Combine like terms: -1x + x = 0
-12 + x2 = -28 + 0 + 2x2
-12 + x2 = -28 + 2x2

Solving
-12 + x2 = -28 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
-12 + x2 + -2x2 = -28 + 2x2 + -2x2

Combine like terms: x2 + -2x2 = -1x2
-12 + -1x2 = -28 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -1x2 = -28 + 0
-12 + -1x2 = -28

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

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

Combine like terms: -28 + 12 = -16
-1x2 = -16

Divide each side by '-1'.
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}

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