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Simplifying (3x + 10)(6x2 + -7x) = 0 Reorder the terms: (10 + 3x)(6x2 + -7x) = 0 Reorder the terms: (10 + 3x)(-7x + 6x2) = 0 Multiply (10 + 3x) * (-7x + 6x2) (10(-7x + 6x2) + 3x * (-7x + 6x2)) = 0 ((-7x * 10 + 6x2 * 10) + 3x * (-7x + 6x2)) = 0 ((-70x + 60x2) + 3x * (-7x + 6x2)) = 0 (-70x + 60x2 + (-7x * 3x + 6x2 * 3x)) = 0 (-70x + 60x2 + (-21x2 + 18x3)) = 0 Combine like terms: 60x2 + -21x2 = 39x2 (-70x + 39x2 + 18x3) = 0 Solving -70x + 39x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-70 + 39x + 18x2) = 0 Factor a trinomial. x((-10 + -3x)(7 + -6x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333Subproblem 3
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, -3.333333333, 1.166666667}
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