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Simplifying (x + 4)(x + -12) = x(x + -9) Reorder the terms: (4 + x)(x + -12) = x(x + -9) Reorder the terms: (4 + x)(-12 + x) = x(x + -9) Multiply (4 + x) * (-12 + x) (4(-12 + x) + x(-12 + x)) = x(x + -9) ((-12 * 4 + x * 4) + x(-12 + x)) = x(x + -9) ((-48 + 4x) + x(-12 + x)) = x(x + -9) (-48 + 4x + (-12 * x + x * x)) = x(x + -9) (-48 + 4x + (-12x + x2)) = x(x + -9) Combine like terms: 4x + -12x = -8x (-48 + -8x + x2) = x(x + -9) Reorder the terms: -48 + -8x + x2 = x(-9 + x) -48 + -8x + x2 = (-9 * x + x * x) -48 + -8x + x2 = (-9x + x2) Add '-1x2' to each side of the equation. -48 + -8x + x2 + -1x2 = -9x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -48 + -8x + 0 = -9x + x2 + -1x2 -48 + -8x = -9x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -48 + -8x = -9x + 0 -48 + -8x = -9x Solving -48 + -8x = -9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9x' to each side of the equation. -48 + -8x + 9x = -9x + 9x Combine like terms: -8x + 9x = 1x -48 + 1x = -9x + 9x Combine like terms: -9x + 9x = 0 -48 + 1x = 0 Add '48' to each side of the equation. -48 + 48 + 1x = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 1x = 0 + 48 1x = 0 + 48 Combine like terms: 0 + 48 = 48 1x = 48 Divide each side by '1'. x = 48 Simplifying x = 48
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