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Simplifying (2x2 + -4x)(6x2 + -5x) = 0 Reorder the terms: (-4x + 2x2)(6x2 + -5x) = 0 Reorder the terms: (-4x + 2x2)(-5x + 6x2) = 0 Multiply (-4x + 2x2) * (-5x + 6x2) (-4x * (-5x + 6x2) + 2x2 * (-5x + 6x2)) = 0 ((-5x * -4x + 6x2 * -4x) + 2x2 * (-5x + 6x2)) = 0 ((20x2 + -24x3) + 2x2 * (-5x + 6x2)) = 0 (20x2 + -24x3 + (-5x * 2x2 + 6x2 * 2x2)) = 0 (20x2 + -24x3 + (-10x3 + 12x4)) = 0 Combine like terms: -24x3 + -10x3 = -34x3 (20x2 + -34x3 + 12x4) = 0 Solving 20x2 + -34x3 + 12x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(10 + -17x + 6x2) = 0 Factor a trinomial. 2x2((5 + -6x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 = 0.8333333333Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, 0.8333333333, 2}
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