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Simplifying 3(2x + 1) + -2x(x + -2) = 3(x + 3) Reorder the terms: 3(1 + 2x) + -2x(x + -2) = 3(x + 3) (1 * 3 + 2x * 3) + -2x(x + -2) = 3(x + 3) (3 + 6x) + -2x(x + -2) = 3(x + 3) Reorder the terms: 3 + 6x + -2x(-2 + x) = 3(x + 3) 3 + 6x + (-2 * -2x + x * -2x) = 3(x + 3) 3 + 6x + (4x + -2x2) = 3(x + 3) Combine like terms: 6x + 4x = 10x 3 + 10x + -2x2 = 3(x + 3) Reorder the terms: 3 + 10x + -2x2 = 3(3 + x) 3 + 10x + -2x2 = (3 * 3 + x * 3) 3 + 10x + -2x2 = (9 + 3x) Solving 3 + 10x + -2x2 = 9 + 3x Solving for variable 'x'. Reorder the terms: 3 + -9 + 10x + -3x + -2x2 = 9 + 3x + -9 + -3x Combine like terms: 3 + -9 = -6 -6 + 10x + -3x + -2x2 = 9 + 3x + -9 + -3x Combine like terms: 10x + -3x = 7x -6 + 7x + -2x2 = 9 + 3x + -9 + -3x Reorder the terms: -6 + 7x + -2x2 = 9 + -9 + 3x + -3x Combine like terms: 9 + -9 = 0 -6 + 7x + -2x2 = 0 + 3x + -3x -6 + 7x + -2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -6 + 7x + -2x2 = 0 Factor a trinomial. (-2 + x)(3 + -2x) = 0Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 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 = {2, 1.5}
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