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Simplifying (x + -3)(4x + -5) + 2(x + -3) = 0 Reorder the terms: (-3 + x)(4x + -5) + 2(x + -3) = 0 Reorder the terms: (-3 + x)(-5 + 4x) + 2(x + -3) = 0 Multiply (-3 + x) * (-5 + 4x) (-3(-5 + 4x) + x(-5 + 4x)) + 2(x + -3) = 0 ((-5 * -3 + 4x * -3) + x(-5 + 4x)) + 2(x + -3) = 0 ((15 + -12x) + x(-5 + 4x)) + 2(x + -3) = 0 (15 + -12x + (-5 * x + 4x * x)) + 2(x + -3) = 0 (15 + -12x + (-5x + 4x2)) + 2(x + -3) = 0 Combine like terms: -12x + -5x = -17x (15 + -17x + 4x2) + 2(x + -3) = 0 Reorder the terms: 15 + -17x + 4x2 + 2(-3 + x) = 0 15 + -17x + 4x2 + (-3 * 2 + x * 2) = 0 15 + -17x + 4x2 + (-6 + 2x) = 0 Reorder the terms: 15 + -6 + -17x + 2x + 4x2 = 0 Combine like terms: 15 + -6 = 9 9 + -17x + 2x + 4x2 = 0 Combine like terms: -17x + 2x = -15x 9 + -15x + 4x2 = 0 Solving 9 + -15x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0.75, 3}
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