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Simplifying 3(5x + 4) * 3(5x + -4) = 2(5x + 4) Reorder the terms: 3(4 + 5x) * 3(5x + -4) = 2(5x + 4) Reorder the terms: 3(4 + 5x) * 3(-4 + 5x) = 2(5x + 4) Reorder the terms for easier multiplication: 3 * 3(4 + 5x)(-4 + 5x) = 2(5x + 4) Multiply 3 * 3 9(4 + 5x)(-4 + 5x) = 2(5x + 4) Multiply (4 + 5x) * (-4 + 5x) 9(4(-4 + 5x) + 5x * (-4 + 5x)) = 2(5x + 4) 9((-4 * 4 + 5x * 4) + 5x * (-4 + 5x)) = 2(5x + 4) 9((-16 + 20x) + 5x * (-4 + 5x)) = 2(5x + 4) 9(-16 + 20x + (-4 * 5x + 5x * 5x)) = 2(5x + 4) 9(-16 + 20x + (-20x + 25x2)) = 2(5x + 4) Combine like terms: 20x + -20x = 0 9(-16 + 0 + 25x2) = 2(5x + 4) 9(-16 + 25x2) = 2(5x + 4) (-16 * 9 + 25x2 * 9) = 2(5x + 4) (-144 + 225x2) = 2(5x + 4) Reorder the terms: -144 + 225x2 = 2(4 + 5x) -144 + 225x2 = (4 * 2 + 5x * 2) -144 + 225x2 = (8 + 10x) Solving -144 + 225x2 = 8 + 10x Solving for variable 'x'. Reorder the terms: -144 + -8 + -10x + 225x2 = 8 + 10x + -8 + -10x Combine like terms: -144 + -8 = -152 -152 + -10x + 225x2 = 8 + 10x + -8 + -10x Reorder the terms: -152 + -10x + 225x2 = 8 + -8 + 10x + -10x Combine like terms: 8 + -8 = 0 -152 + -10x + 225x2 = 0 + 10x + -10x -152 + -10x + 225x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -152 + -10x + 225x2 = 0 Factor a trinomial. (-4 + -5x)(38 + -45x) = 0Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8Subproblem 2
Set the factor '(38 + -45x)' equal to zero and attempt to solve: Simplifying 38 + -45x = 0 Solving 38 + -45x = 0 Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + -45x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -45x = 0 + -38 -45x = 0 + -38 Combine like terms: 0 + -38 = -38 -45x = -38 Divide each side by '-45'. x = 0.8444444444 Simplifying x = 0.8444444444Solution
x = {-0.8, 0.8444444444}
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