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Simplifying (2x + 3)(x + -6) + -2x2 + 3x + 30 = 0 Reorder the terms: (3 + 2x)(x + -6) + -2x2 + 3x + 30 = 0 Reorder the terms: (3 + 2x)(-6 + x) + -2x2 + 3x + 30 = 0 Multiply (3 + 2x) * (-6 + x) (3(-6 + x) + 2x * (-6 + x)) + -2x2 + 3x + 30 = 0 ((-6 * 3 + x * 3) + 2x * (-6 + x)) + -2x2 + 3x + 30 = 0 ((-18 + 3x) + 2x * (-6 + x)) + -2x2 + 3x + 30 = 0 (-18 + 3x + (-6 * 2x + x * 2x)) + -2x2 + 3x + 30 = 0 (-18 + 3x + (-12x + 2x2)) + -2x2 + 3x + 30 = 0 Combine like terms: 3x + -12x = -9x (-18 + -9x + 2x2) + -2x2 + 3x + 30 = 0 Reorder the terms: -18 + 30 + -9x + 3x + 2x2 + -2x2 = 0 Combine like terms: -18 + 30 = 12 12 + -9x + 3x + 2x2 + -2x2 = 0 Combine like terms: -9x + 3x = -6x 12 + -6x + 2x2 + -2x2 = 0 Combine like terms: 2x2 + -2x2 = 0 12 + -6x + 0 = 0 12 + -6x = 0 Solving 12 + -6x = 0 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 + -6x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6x = 0 + -12 -6x = 0 + -12 Combine like terms: 0 + -12 = -12 -6x = -12 Divide each side by '-6'. x = 2 Simplifying x = 2
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