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Simplifying 3 + (2x + -3)(4 + -5x) = 0 Reorder the terms: 3 + (-3 + 2x)(4 + -5x) = 0 Multiply (-3 + 2x) * (4 + -5x) 3 + (-3(4 + -5x) + 2x * (4 + -5x)) = 0 3 + ((4 * -3 + -5x * -3) + 2x * (4 + -5x)) = 0 3 + ((-12 + 15x) + 2x * (4 + -5x)) = 0 3 + (-12 + 15x + (4 * 2x + -5x * 2x)) = 0 3 + (-12 + 15x + (8x + -10x2)) = 0 Combine like terms: 15x + 8x = 23x 3 + (-12 + 23x + -10x2) = 0 Combine like terms: 3 + -12 = -9 -9 + 23x + -10x2 = 0 Solving -9 + 23x + -10x2 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + 5x)(1 + -2x) = 0Subproblem 1
Set the factor '(-9 + 5x)' equal to zero and attempt to solve: Simplifying -9 + 5x = 0 Solving -9 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5x = 0 + 9 5x = 0 + 9 Combine like terms: 0 + 9 = 9 5x = 9 Divide each side by '5'. x = 1.8 Simplifying x = 1.8Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {1.8, 0.5}
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