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

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


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

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

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

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

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

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

Solving for variable 'x'.

Reorder the terms:
-15 + -209 + -8x + 16x2 = 209 + -209

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

Combine like terms: 209 + -209 = 0
-224 + -8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-28 + -1x + 2x2) = 0

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

Ignore the factor 8.

Subproblem 1
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

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 = {-3.5, 4}

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