209=(4x+3)(4x-5)

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Solution for 209=(4x+3)(4x-5) equation: 


Simplifying
209 = (4x + 3)(4x + -5)

Reorder the terms:
209 = (3 + 4x)(4x + -5)

Reorder the terms:
209 = (3 + 4x)(-5 + 4x)

Multiply (3 + 4x) * (-5 + 4x)
209 = (3(-5 + 4x) + 4x * (-5 + 4x))
209 = ((-5 * 3 + 4x * 3) + 4x * (-5 + 4x))
209 = ((-15 + 12x) + 4x * (-5 + 4x))
209 = (-15 + 12x + (-5 * 4x + 4x * 4x))
209 = (-15 + 12x + (-20x + 16x2))

Combine like terms: 12x + -20x = -8x
209 = (-15 + -8x + 16x2)

Solving
209 = -15 + -8x + 16x2

Solving for variable 'x'.

Combine like terms: 209 + 15 = 224
224 + 8x + -16x2 = -15 + -8x + 16x2 + 15 + 8x + -16x2

Reorder the terms:
224 + 8x + -16x2 = -15 + 15 + -8x + 8x + 16x2 + -16x2

Combine like terms: -15 + 15 = 0
224 + 8x + -16x2 = 0 + -8x + 8x + 16x2 + -16x2
224 + 8x + -16x2 = -8x + 8x + 16x2 + -16x2

Combine like terms: -8x + 8x = 0
224 + 8x + -16x2 = 0 + 16x2 + -16x2
224 + 8x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
224 + 8x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(28 + x + -2x2) = 0

Factor a trinomial.
8((4 + -1x)(7 + 2x)) = 0

Ignore the factor 8.

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 '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {4, -3.5}

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