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Simplifying 12x2 + -7x + -12 = (4x + 3)(3x + -7) Reorder the terms: -12 + -7x + 12x2 = (4x + 3)(3x + -7) Reorder the terms: -12 + -7x + 12x2 = (3 + 4x)(3x + -7) Reorder the terms: -12 + -7x + 12x2 = (3 + 4x)(-7 + 3x) Multiply (3 + 4x) * (-7 + 3x) -12 + -7x + 12x2 = (3(-7 + 3x) + 4x * (-7 + 3x)) -12 + -7x + 12x2 = ((-7 * 3 + 3x * 3) + 4x * (-7 + 3x)) -12 + -7x + 12x2 = ((-21 + 9x) + 4x * (-7 + 3x)) -12 + -7x + 12x2 = (-21 + 9x + (-7 * 4x + 3x * 4x)) -12 + -7x + 12x2 = (-21 + 9x + (-28x + 12x2)) Combine like terms: 9x + -28x = -19x -12 + -7x + 12x2 = (-21 + -19x + 12x2) Add '-12x2' to each side of the equation. -12 + -7x + 12x2 + -12x2 = -21 + -19x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -7x + 0 = -21 + -19x + 12x2 + -12x2 -12 + -7x = -21 + -19x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -7x = -21 + -19x + 0 -12 + -7x = -21 + -19x Solving -12 + -7x = -21 + -19x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19x' to each side of the equation. -12 + -7x + 19x = -21 + -19x + 19x Combine like terms: -7x + 19x = 12x -12 + 12x = -21 + -19x + 19x Combine like terms: -19x + 19x = 0 -12 + 12x = -21 + 0 -12 + 12x = -21 Add '12' to each side of the equation. -12 + 12 + 12x = -21 + 12 Combine like terms: -12 + 12 = 0 0 + 12x = -21 + 12 12x = -21 + 12 Combine like terms: -21 + 12 = -9 12x = -9 Divide each side by '12'. x = -0.75 Simplifying x = -0.75
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