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

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


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

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

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

Multiply (4 + 3x) * (-4 + x)
(4(-4 + x) + 3x * (-4 + x)) = (7 + -3x)(x + -4)
((-4 * 4 + x * 4) + 3x * (-4 + x)) = (7 + -3x)(x + -4)
((-16 + 4x) + 3x * (-4 + x)) = (7 + -3x)(x + -4)
(-16 + 4x + (-4 * 3x + x * 3x)) = (7 + -3x)(x + -4)
(-16 + 4x + (-12x + 3x2)) = (7 + -3x)(x + -4)

Combine like terms: 4x + -12x = -8x
(-16 + -8x + 3x2) = (7 + -3x)(x + -4)

Reorder the terms:
-16 + -8x + 3x2 = (7 + -3x)(-4 + x)

Multiply (7 + -3x) * (-4 + x)
-16 + -8x + 3x2 = (7(-4 + x) + -3x * (-4 + x))
-16 + -8x + 3x2 = ((-4 * 7 + x * 7) + -3x * (-4 + x))
-16 + -8x + 3x2 = ((-28 + 7x) + -3x * (-4 + x))
-16 + -8x + 3x2 = (-28 + 7x + (-4 * -3x + x * -3x))
-16 + -8x + 3x2 = (-28 + 7x + (12x + -3x2))

Combine like terms: 7x + 12x = 19x
-16 + -8x + 3x2 = (-28 + 19x + -3x2)

Solving
-16 + -8x + 3x2 = -28 + 19x + -3x2

Solving for variable 'x'.

Reorder the terms:
-16 + 28 + -8x + -19x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: -16 + 28 = 12
12 + -8x + -19x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: -8x + -19x = -27x
12 + -27x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
12 + -27x + 6x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Reorder the terms:
12 + -27x + 6x2 = -28 + 28 + 19x + -19x + -3x2 + 3x2

Combine like terms: -28 + 28 = 0
12 + -27x + 6x2 = 0 + 19x + -19x + -3x2 + 3x2
12 + -27x + 6x2 = 19x + -19x + -3x2 + 3x2

Combine like terms: 19x + -19x = 0
12 + -27x + 6x2 = 0 + -3x2 + 3x2
12 + -27x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12 + -27x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -9x + 2x2) = 0

Factor a trinomial.
3((1 + -2x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.5, 4}

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