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Simplifying 5x(6x + 1) + 1(6x + 1) = 0 Reorder the terms: 5x(1 + 6x) + 1(6x + 1) = 0 (1 * 5x + 6x * 5x) + 1(6x + 1) = 0 (5x + 30x2) + 1(6x + 1) = 0 Reorder the terms: 5x + 30x2 + 1(1 + 6x) = 0 5x + 30x2 + (1 * 1 + 6x * 1) = 0 5x + 30x2 + (1 + 6x) = 0 Reorder the terms: 1 + 5x + 6x + 30x2 = 0 Combine like terms: 5x + 6x = 11x 1 + 11x + 30x2 = 0 Solving 1 + 11x + 30x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + 5x)(1 + 6x) = 0Subproblem 1
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-0.2, -0.1666666667}
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