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Simplifying (-9x + 6)(-8x + -7) + -1(-9x + 6)(4x + -3) = 0 Reorder the terms: (6 + -9x)(-8x + -7) + -1(-9x + 6)(4x + -3) = 0 Reorder the terms: (6 + -9x)(-7 + -8x) + -1(-9x + 6)(4x + -3) = 0 Multiply (6 + -9x) * (-7 + -8x) (6(-7 + -8x) + -9x * (-7 + -8x)) + -1(-9x + 6)(4x + -3) = 0 ((-7 * 6 + -8x * 6) + -9x * (-7 + -8x)) + -1(-9x + 6)(4x + -3) = 0 ((-42 + -48x) + -9x * (-7 + -8x)) + -1(-9x + 6)(4x + -3) = 0 (-42 + -48x + (-7 * -9x + -8x * -9x)) + -1(-9x + 6)(4x + -3) = 0 (-42 + -48x + (63x + 72x2)) + -1(-9x + 6)(4x + -3) = 0 Combine like terms: -48x + 63x = 15x (-42 + 15x + 72x2) + -1(-9x + 6)(4x + -3) = 0 Reorder the terms: -42 + 15x + 72x2 + -1(6 + -9x)(4x + -3) = 0 Reorder the terms: -42 + 15x + 72x2 + -1(6 + -9x)(-3 + 4x) = 0 Multiply (6 + -9x) * (-3 + 4x) -42 + 15x + 72x2 + -1(6(-3 + 4x) + -9x * (-3 + 4x)) = 0 -42 + 15x + 72x2 + -1((-3 * 6 + 4x * 6) + -9x * (-3 + 4x)) = 0 -42 + 15x + 72x2 + -1((-18 + 24x) + -9x * (-3 + 4x)) = 0 -42 + 15x + 72x2 + -1(-18 + 24x + (-3 * -9x + 4x * -9x)) = 0 -42 + 15x + 72x2 + -1(-18 + 24x + (27x + -36x2)) = 0 Combine like terms: 24x + 27x = 51x -42 + 15x + 72x2 + -1(-18 + 51x + -36x2) = 0 -42 + 15x + 72x2 + (-18 * -1 + 51x * -1 + -36x2 * -1) = 0 -42 + 15x + 72x2 + (18 + -51x + 36x2) = 0 Reorder the terms: -42 + 18 + 15x + -51x + 72x2 + 36x2 = 0 Combine like terms: -42 + 18 = -24 -24 + 15x + -51x + 72x2 + 36x2 = 0 Combine like terms: 15x + -51x = -36x -24 + -36x + 72x2 + 36x2 = 0 Combine like terms: 72x2 + 36x2 = 108x2 -24 + -36x + 108x2 = 0 Solving -24 + -36x + 108x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + -3x + 9x2) = 0 Factor a trinomial. 12((-1 + -3x)(2 + -3x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.3333333333, 0.6666666667}
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