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

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


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

Reorder the terms:
(5 + 4x)(4x + -4) = 3x(21)

Reorder the terms:
(5 + 4x)(-4 + 4x) = 3x(21)

Multiply (5 + 4x) * (-4 + 4x)
(5(-4 + 4x) + 4x * (-4 + 4x)) = 3x(21)
((-4 * 5 + 4x * 5) + 4x * (-4 + 4x)) = 3x(21)
((-20 + 20x) + 4x * (-4 + 4x)) = 3x(21)
(-20 + 20x + (-4 * 4x + 4x * 4x)) = 3x(21)
(-20 + 20x + (-16x + 16x2)) = 3x(21)

Combine like terms: 20x + -16x = 4x
(-20 + 4x + 16x2) = 3x(21)

Reorder the terms for easier multiplication:
-20 + 4x + 16x2 = 3 * 21x

Multiply 3 * 21
-20 + 4x + 16x2 = 63x

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

Solving for variable 'x'.

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

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

Combine like terms: 63x + -63x = 0
-20 + -59x + 16x2 = 0

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


Subproblem 1
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

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 = {-0.3125, 4}

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