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Simplifying (7x + -2) * x(-5x + 3) = 0 Reorder the terms: (-2 + 7x) * x(-5x + 3) = 0 Reorder the terms: (-2 + 7x) * x(3 + -5x) = 0 Reorder the terms for easier multiplication: x(-2 + 7x)(3 + -5x) = 0 Multiply (-2 + 7x) * (3 + -5x) x(-2(3 + -5x) + 7x * (3 + -5x)) = 0 x((3 * -2 + -5x * -2) + 7x * (3 + -5x)) = 0 x((-6 + 10x) + 7x * (3 + -5x)) = 0 x(-6 + 10x + (3 * 7x + -5x * 7x)) = 0 x(-6 + 10x + (21x + -35x2)) = 0 Combine like terms: 10x + 21x = 31x x(-6 + 31x + -35x2) = 0 (-6 * x + 31x * x + -35x2 * x) = 0 (-6x + 31x2 + -35x3) = 0 Solving -6x + 31x2 + -35x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 31x + -35x2) = 0 Factor a trinomial. x((-3 + 5x)(2 + -7x)) = 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 '(-3 + 5x)' equal to zero and attempt to solve: Simplifying -3 + 5x = 0 Solving -3 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x = 0 + 3 5x = 0 + 3 Combine like terms: 0 + 3 = 3 5x = 3 Divide each side by '5'. x = 0.6 Simplifying x = 0.6Subproblem 3
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {0, 0.6, 0.2857142857}
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