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Simplifying (6x + 7)(1 + -4x) = 0 Reorder the terms: (7 + 6x)(1 + -4x) = 0 Multiply (7 + 6x) * (1 + -4x) (7(1 + -4x) + 6x * (1 + -4x)) = 0 ((1 * 7 + -4x * 7) + 6x * (1 + -4x)) = 0 ((7 + -28x) + 6x * (1 + -4x)) = 0 (7 + -28x + (1 * 6x + -4x * 6x)) = 0 (7 + -28x + (6x + -24x2)) = 0 Combine like terms: -28x + 6x = -22x (7 + -22x + -24x2) = 0 Solving 7 + -22x + -24x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -4x)(7 + 6x) = 0Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667Solution
x = {0.25, -1.166666667}
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