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Simplifying (8x + -6)(4x + -2) = 32x * x + 52 Reorder the terms: (-6 + 8x)(4x + -2) = 32x * x + 52 Reorder the terms: (-6 + 8x)(-2 + 4x) = 32x * x + 52 Multiply (-6 + 8x) * (-2 + 4x) (-6(-2 + 4x) + 8x * (-2 + 4x)) = 32x * x + 52 ((-2 * -6 + 4x * -6) + 8x * (-2 + 4x)) = 32x * x + 52 ((12 + -24x) + 8x * (-2 + 4x)) = 32x * x + 52 (12 + -24x + (-2 * 8x + 4x * 8x)) = 32x * x + 52 (12 + -24x + (-16x + 32x2)) = 32x * x + 52 Combine like terms: -24x + -16x = -40x (12 + -40x + 32x2) = 32x * x + 52 Multiply x * x 12 + -40x + 32x2 = 32x2 + 52 Reorder the terms: 12 + -40x + 32x2 = 52 + 32x2 Add '-32x2' to each side of the equation. 12 + -40x + 32x2 + -32x2 = 52 + 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 12 + -40x + 0 = 52 + 32x2 + -32x2 12 + -40x = 52 + 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 12 + -40x = 52 + 0 12 + -40x = 52 Solving 12 + -40x = 52 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -40x = 52 + -12 Combine like terms: 12 + -12 = 0 0 + -40x = 52 + -12 -40x = 52 + -12 Combine like terms: 52 + -12 = 40 -40x = 40 Divide each side by '-40'. x = -1 Simplifying x = -1
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