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Simplifying (6x + -7)(9x + 8) = 7 + -18x(2 + -3x) Reorder the terms: (-7 + 6x)(9x + 8) = 7 + -18x(2 + -3x) Reorder the terms: (-7 + 6x)(8 + 9x) = 7 + -18x(2 + -3x) Multiply (-7 + 6x) * (8 + 9x) (-7(8 + 9x) + 6x * (8 + 9x)) = 7 + -18x(2 + -3x) ((8 * -7 + 9x * -7) + 6x * (8 + 9x)) = 7 + -18x(2 + -3x) ((-56 + -63x) + 6x * (8 + 9x)) = 7 + -18x(2 + -3x) (-56 + -63x + (8 * 6x + 9x * 6x)) = 7 + -18x(2 + -3x) (-56 + -63x + (48x + 54x2)) = 7 + -18x(2 + -3x) Combine like terms: -63x + 48x = -15x (-56 + -15x + 54x2) = 7 + -18x(2 + -3x) -56 + -15x + 54x2 = 7 + (2 * -18x + -3x * -18x) -56 + -15x + 54x2 = 7 + (-36x + 54x2) Add '-54x2' to each side of the equation. -56 + -15x + 54x2 + -54x2 = 7 + -36x + 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -56 + -15x + 0 = 7 + -36x + 54x2 + -54x2 -56 + -15x = 7 + -36x + 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -56 + -15x = 7 + -36x + 0 -56 + -15x = 7 + -36x Solving -56 + -15x = 7 + -36x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36x' to each side of the equation. -56 + -15x + 36x = 7 + -36x + 36x Combine like terms: -15x + 36x = 21x -56 + 21x = 7 + -36x + 36x Combine like terms: -36x + 36x = 0 -56 + 21x = 7 + 0 -56 + 21x = 7 Add '56' to each side of the equation. -56 + 56 + 21x = 7 + 56 Combine like terms: -56 + 56 = 0 0 + 21x = 7 + 56 21x = 7 + 56 Combine like terms: 7 + 56 = 63 21x = 63 Divide each side by '21'. x = 3 Simplifying x = 3
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