3x(21)=(4x+5)(4x-4)

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Solution for 3x(21)=(4x+5)(4x-4) equation: 


Simplifying
3x(21) = (4x + 5)(4x + -4)

Reorder the terms for easier multiplication:
3 * 21x = (4x + 5)(4x + -4)

Multiply 3 * 21
63x = (4x + 5)(4x + -4)

Reorder the terms:
63x = (5 + 4x)(4x + -4)

Reorder the terms:
63x = (5 + 4x)(-4 + 4x)

Multiply (5 + 4x) * (-4 + 4x)
63x = (5(-4 + 4x) + 4x * (-4 + 4x))
63x = ((-4 * 5 + 4x * 5) + 4x * (-4 + 4x))
63x = ((-20 + 20x) + 4x * (-4 + 4x))
63x = (-20 + 20x + (-4 * 4x + 4x * 4x))
63x = (-20 + 20x + (-16x + 16x2))

Combine like terms: 20x + -16x = 4x
63x = (-20 + 4x + 16x2)

Solving
63x = -20 + 4x + 16x2

Solving for variable 'x'.

Reorder the terms:
20 + 63x + -4x + -16x2 = -20 + 4x + 16x2 + 20 + -4x + -16x2

Combine like terms: 63x + -4x = 59x
20 + 59x + -16x2 = -20 + 4x + 16x2 + 20 + -4x + -16x2

Reorder the terms:
20 + 59x + -16x2 = -20 + 20 + 4x + -4x + 16x2 + -16x2

Combine like terms: -20 + 20 = 0
20 + 59x + -16x2 = 0 + 4x + -4x + 16x2 + -16x2
20 + 59x + -16x2 = 4x + -4x + 16x2 + -16x2

Combine like terms: 4x + -4x = 0
20 + 59x + -16x2 = 0 + 16x2 + -16x2
20 + 59x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
20 + 59x + -16x2 = 0

Factor a trinomial.
(4 + -1x)(5 + 16x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 16x)' equal to zero and attempt to solve:

Simplifying
5 + 16x = 0

Solving
5 + 16x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 16x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 16x = 0 + -5
16x = 0 + -5

Combine like terms: 0 + -5 = -5
16x = -5

Divide each side by '16'.
x = -0.3125

Simplifying
x = -0.3125
Solution
x = {4, -0.3125}

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