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Simplifying 7x(2x + 3) + (2x + 3) = 0 Reorder the terms: 7x(3 + 2x) + (2x + 3) = 0 (3 * 7x + 2x * 7x) + (2x + 3) = 0 (21x + 14x2) + (2x + 3) = 0 Reorder the terms: 21x + 14x2 + (3 + 2x) = 0 Remove parenthesis around (3 + 2x) 21x + 14x2 + 3 + 2x = 0 Reorder the terms: 3 + 21x + 2x + 14x2 = 0 Combine like terms: 21x + 2x = 23x 3 + 23x + 14x2 = 0 Solving 3 + 23x + 14x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(1 + 7x) = 0Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve: Simplifying 1 + 7x = 0 Solving 1 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x = 0 + -1 7x = 0 + -1 Combine like terms: 0 + -1 = -1 7x = -1 Divide each side by '7'. x = -0.1428571429 Simplifying x = -0.1428571429Solution
x = {-1.5, -0.1428571429}
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