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Simplifying 10(x + 4 + -9)(x + -3) = 8(x + 3) Reorder the terms: 10(4 + -9 + x)(x + -3) = 8(x + 3) Combine like terms: 4 + -9 = -5 10(-5 + x)(x + -3) = 8(x + 3) Reorder the terms: 10(-5 + x)(-3 + x) = 8(x + 3) Multiply (-5 + x) * (-3 + x) 10(-5(-3 + x) + x(-3 + x)) = 8(x + 3) 10((-3 * -5 + x * -5) + x(-3 + x)) = 8(x + 3) 10((15 + -5x) + x(-3 + x)) = 8(x + 3) 10(15 + -5x + (-3 * x + x * x)) = 8(x + 3) 10(15 + -5x + (-3x + x2)) = 8(x + 3) Combine like terms: -5x + -3x = -8x 10(15 + -8x + x2) = 8(x + 3) (15 * 10 + -8x * 10 + x2 * 10) = 8(x + 3) (150 + -80x + 10x2) = 8(x + 3) Reorder the terms: 150 + -80x + 10x2 = 8(3 + x) 150 + -80x + 10x2 = (3 * 8 + x * 8) 150 + -80x + 10x2 = (24 + 8x) Solving 150 + -80x + 10x2 = 24 + 8x Solving for variable 'x'. Reorder the terms: 150 + -24 + -80x + -8x + 10x2 = 24 + 8x + -24 + -8x Combine like terms: 150 + -24 = 126 126 + -80x + -8x + 10x2 = 24 + 8x + -24 + -8x Combine like terms: -80x + -8x = -88x 126 + -88x + 10x2 = 24 + 8x + -24 + -8x Reorder the terms: 126 + -88x + 10x2 = 24 + -24 + 8x + -8x Combine like terms: 24 + -24 = 0 126 + -88x + 10x2 = 0 + 8x + -8x 126 + -88x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 126 + -88x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(63 + -44x + 5x2) = 0 Factor a trinomial. 2((9 + -5x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1.8, 7}
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