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Simplifying (3x + 4)(6x + -5) = 0 Reorder the terms: (4 + 3x)(6x + -5) = 0 Reorder the terms: (4 + 3x)(-5 + 6x) = 0 Multiply (4 + 3x) * (-5 + 6x) (4(-5 + 6x) + 3x * (-5 + 6x)) = 0 ((-5 * 4 + 6x * 4) + 3x * (-5 + 6x)) = 0 ((-20 + 24x) + 3x * (-5 + 6x)) = 0 (-20 + 24x + (-5 * 3x + 6x * 3x)) = 0 (-20 + 24x + (-15x + 18x2)) = 0 Combine like terms: 24x + -15x = 9x (-20 + 9x + 18x2) = 0 Solving -20 + 9x + 18x2 = 0 Solving for variable 'x'. Factor a trinomial. (-4 + -3x)(5 + -6x) = 0Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {-1.333333333, 0.8333333333}
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