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Simplifying 10xy + 15by + -8x + -12b = (2x + 3b)(5y + -4) Reorder the terms: -12b + 15by + -8x + 10xy = (2x + 3b)(5y + -4) Reorder the terms: -12b + 15by + -8x + 10xy = (3b + 2x)(5y + -4) Reorder the terms: -12b + 15by + -8x + 10xy = (3b + 2x)(-4 + 5y) Multiply (3b + 2x) * (-4 + 5y) -12b + 15by + -8x + 10xy = (3b * (-4 + 5y) + 2x * (-4 + 5y)) -12b + 15by + -8x + 10xy = ((-4 * 3b + 5y * 3b) + 2x * (-4 + 5y)) -12b + 15by + -8x + 10xy = ((-12b + 15by) + 2x * (-4 + 5y)) -12b + 15by + -8x + 10xy = (-12b + 15by + (-4 * 2x + 5y * 2x)) -12b + 15by + -8x + 10xy = (-12b + 15by + (-8x + 10xy)) -12b + 15by + -8x + 10xy = (-12b + 15by + -8x + 10xy) Add '12b' to each side of the equation. -12b + 15by + -8x + 12b + 10xy = -12b + 15by + -8x + 12b + 10xy Reorder the terms: -12b + 12b + 15by + -8x + 10xy = -12b + 15by + -8x + 12b + 10xy Combine like terms: -12b + 12b = 0 0 + 15by + -8x + 10xy = -12b + 15by + -8x + 12b + 10xy 15by + -8x + 10xy = -12b + 15by + -8x + 12b + 10xy Reorder the terms: 15by + -8x + 10xy = -12b + 12b + 15by + -8x + 10xy Combine like terms: -12b + 12b = 0 15by + -8x + 10xy = 0 + 15by + -8x + 10xy 15by + -8x + 10xy = 15by + -8x + 10xy Add '-15by' to each side of the equation. 15by + -8x + -15by + 10xy = 15by + -8x + -15by + 10xy Reorder the terms: 15by + -15by + -8x + 10xy = 15by + -8x + -15by + 10xy Combine like terms: 15by + -15by = 0 0 + -8x + 10xy = 15by + -8x + -15by + 10xy -8x + 10xy = 15by + -8x + -15by + 10xy Reorder the terms: -8x + 10xy = 15by + -15by + -8x + 10xy Combine like terms: 15by + -15by = 0 -8x + 10xy = 0 + -8x + 10xy -8x + 10xy = -8x + 10xy Add '8x' to each side of the equation. -8x + 8x + 10xy = -8x + 8x + 10xy Combine like terms: -8x + 8x = 0 0 + 10xy = -8x + 8x + 10xy 10xy = -8x + 8x + 10xy Combine like terms: -8x + 8x = 0 10xy = 0 + 10xy 10xy = 10xy Add '-10xy' to each side of the equation. 10xy + -10xy = 10xy + -10xy Combine like terms: 10xy + -10xy = 0 0 = 10xy + -10xy Combine like terms: 10xy + -10xy = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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