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Simplifying (2x + -3)(4 + 7x) + (2x + -3)(x + -4) = 0 Reorder the terms: (-3 + 2x)(4 + 7x) + (2x + -3)(x + -4) = 0 Multiply (-3 + 2x) * (4 + 7x) (-3(4 + 7x) + 2x * (4 + 7x)) + (2x + -3)(x + -4) = 0 ((4 * -3 + 7x * -3) + 2x * (4 + 7x)) + (2x + -3)(x + -4) = 0 ((-12 + -21x) + 2x * (4 + 7x)) + (2x + -3)(x + -4) = 0 (-12 + -21x + (4 * 2x + 7x * 2x)) + (2x + -3)(x + -4) = 0 (-12 + -21x + (8x + 14x2)) + (2x + -3)(x + -4) = 0 Combine like terms: -21x + 8x = -13x (-12 + -13x + 14x2) + (2x + -3)(x + -4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-3 + 2x)(x + -4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-3 + 2x)(-4 + x) = 0 Multiply (-3 + 2x) * (-4 + x) -12 + -13x + 14x2 + (-3(-4 + x) + 2x * (-4 + x)) = 0 -12 + -13x + 14x2 + ((-4 * -3 + x * -3) + 2x * (-4 + x)) = 0 -12 + -13x + 14x2 + ((12 + -3x) + 2x * (-4 + x)) = 0 -12 + -13x + 14x2 + (12 + -3x + (-4 * 2x + x * 2x)) = 0 -12 + -13x + 14x2 + (12 + -3x + (-8x + 2x2)) = 0 Combine like terms: -3x + -8x = -11x -12 + -13x + 14x2 + (12 + -11x + 2x2) = 0 Reorder the terms: -12 + 12 + -13x + -11x + 14x2 + 2x2 = 0 Combine like terms: -12 + 12 = 0 0 + -13x + -11x + 14x2 + 2x2 = 0 -13x + -11x + 14x2 + 2x2 = 0 Combine like terms: -13x + -11x = -24x -24x + 14x2 + 2x2 = 0 Combine like terms: 14x2 + 2x2 = 16x2 -24x + 16x2 = 0 Solving -24x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(-3 + 2x) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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