(4x+7)(5x-4)=209

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Solution for (4x+7)(5x-4)=209 equation: 


Simplifying
(4x + 7)(5x + -4) = 209

Reorder the terms:
(7 + 4x)(5x + -4) = 209

Reorder the terms:
(7 + 4x)(-4 + 5x) = 209

Multiply (7 + 4x) * (-4 + 5x)
(7(-4 + 5x) + 4x * (-4 + 5x)) = 209
((-4 * 7 + 5x * 7) + 4x * (-4 + 5x)) = 209
((-28 + 35x) + 4x * (-4 + 5x)) = 209
(-28 + 35x + (-4 * 4x + 5x * 4x)) = 209
(-28 + 35x + (-16x + 20x2)) = 209

Combine like terms: 35x + -16x = 19x
(-28 + 19x + 20x2) = 209

Solving
-28 + 19x + 20x2 = 209

Solving for variable 'x'.

Reorder the terms:
-28 + -209 + 19x + 20x2 = 209 + -209

Combine like terms: -28 + -209 = -237
-237 + 19x + 20x2 = 209 + -209

Combine like terms: 209 + -209 = 0
-237 + 19x + 20x2 = 0

Factor a trinomial.
(-79 + -20x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-79 + -20x)' equal to zero and attempt to solve:

Simplifying
-79 + -20x = 0

Solving
-79 + -20x = 0

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

Add '79' to each side of the equation.
-79 + 79 + -20x = 0 + 79

Combine like terms: -79 + 79 = 0
0 + -20x = 0 + 79
-20x = 0 + 79

Combine like terms: 0 + 79 = 79
-20x = 79

Divide each side by '-20'.
x = -3.95

Simplifying
x = -3.95

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.95, 3}

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