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Simplifying (6x2 + -5x3) + -1(3x2 + -7x3) = 0 Remove parenthesis around (6x2 + -5x3) 6x2 + -5x3 + -1(3x2 + -7x3) = 0 6x2 + -5x3 + (3x2 * -1 + -7x3 * -1) = 0 6x2 + -5x3 + (-3x2 + 7x3) = 0 Reorder the terms: 6x2 + -3x2 + -5x3 + 7x3 = 0 Combine like terms: 6x2 + -3x2 = 3x2 3x2 + -5x3 + 7x3 = 0 Combine like terms: -5x3 + 7x3 = 2x3 3x2 + 2x3 = 0 Solving 3x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(3 + 2x) = 0Subproblem 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -1.5}
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