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Simplifying (x + -4)(3x + 5) = (x + 10)(x + -2) Reorder the terms: (-4 + x)(3x + 5) = (x + 10)(x + -2) Reorder the terms: (-4 + x)(5 + 3x) = (x + 10)(x + -2) Multiply (-4 + x) * (5 + 3x) (-4(5 + 3x) + x(5 + 3x)) = (x + 10)(x + -2) ((5 * -4 + 3x * -4) + x(5 + 3x)) = (x + 10)(x + -2) ((-20 + -12x) + x(5 + 3x)) = (x + 10)(x + -2) (-20 + -12x + (5 * x + 3x * x)) = (x + 10)(x + -2) (-20 + -12x + (5x + 3x2)) = (x + 10)(x + -2) Combine like terms: -12x + 5x = -7x (-20 + -7x + 3x2) = (x + 10)(x + -2) Reorder the terms: -20 + -7x + 3x2 = (10 + x)(x + -2) Reorder the terms: -20 + -7x + 3x2 = (10 + x)(-2 + x) Multiply (10 + x) * (-2 + x) -20 + -7x + 3x2 = (10(-2 + x) + x(-2 + x)) -20 + -7x + 3x2 = ((-2 * 10 + x * 10) + x(-2 + x)) -20 + -7x + 3x2 = ((-20 + 10x) + x(-2 + x)) -20 + -7x + 3x2 = (-20 + 10x + (-2 * x + x * x)) -20 + -7x + 3x2 = (-20 + 10x + (-2x + x2)) Combine like terms: 10x + -2x = 8x -20 + -7x + 3x2 = (-20 + 8x + x2) Add '20' to each side of the equation. -20 + -7x + 20 + 3x2 = -20 + 8x + 20 + x2 Reorder the terms: -20 + 20 + -7x + 3x2 = -20 + 8x + 20 + x2 Combine like terms: -20 + 20 = 0 0 + -7x + 3x2 = -20 + 8x + 20 + x2 -7x + 3x2 = -20 + 8x + 20 + x2 Reorder the terms: -7x + 3x2 = -20 + 20 + 8x + x2 Combine like terms: -20 + 20 = 0 -7x + 3x2 = 0 + 8x + x2 -7x + 3x2 = 8x + x2 Solving -7x + 3x2 = 8x + x2 Solving for variable 'x'. Reorder the terms: -7x + -8x + 3x2 + -1x2 = 8x + x2 + -8x + -1x2 Combine like terms: -7x + -8x = -15x -15x + 3x2 + -1x2 = 8x + x2 + -8x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -15x + 2x2 = 8x + x2 + -8x + -1x2 Reorder the terms: -15x + 2x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -15x + 2x2 = 0 + x2 + -1x2 -15x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Divide each side by '2'. x = 7.5 Simplifying x = 7.5Solution
x = {0, 7.5}
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