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Simplifying
(3x + 5)(x + 4) = 17x + 67
Reorder the terms:
(5 + 3x)(x + 4) = 17x + 67
Reorder the terms:
(5 + 3x)(4 + x) = 17x + 67
Multiply (5 + 3x) * (4 + x)
(5(4 + x) + 3x * (4 + x)) = 17x + 67
((4 * 5 + x * 5) + 3x * (4 + x)) = 17x + 67
((20 + 5x) + 3x * (4 + x)) = 17x + 67
(20 + 5x + (4 * 3x + x * 3x)) = 17x + 67
(20 + 5x + (12x + 3x2)) = 17x + 67
Combine like terms: 5x + 12x = 17x
(20 + 17x + 3x2) = 17x + 67
Reorder the terms:
20 + 17x + 3x2 = 67 + 17x
Add '-17x' to each side of the equation.
20 + 17x + -17x + 3x2 = 67 + 17x + -17x
Combine like terms: 17x + -17x = 0
20 + 0 + 3x2 = 67 + 17x + -17x
20 + 3x2 = 67 + 17x + -17x
Combine like terms: 17x + -17x = 0
20 + 3x2 = 67 + 0
20 + 3x2 = 67
Solving
20 + 3x2 = 67
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + 3x2 = 67 + -20
Combine like terms: 20 + -20 = 0
0 + 3x2 = 67 + -20
3x2 = 67 + -20
Combine like terms: 67 + -20 = 47
3x2 = 47
Divide each side by '3'.
x2 = 15.66666667
Simplifying
x2 = 15.66666667
Take the square root of each side:
x = {-3.958114029, 3.958114029}
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