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Simplifying -2x + 4 = 2(4x + -3) * 3(-8 + 4x) Reorder the terms: 4 + -2x = 2(4x + -3) * 3(-8 + 4x) Reorder the terms: 4 + -2x = 2(-3 + 4x) * 3(-8 + 4x) Reorder the terms for easier multiplication: 4 + -2x = 2 * 3(-3 + 4x)(-8 + 4x) Multiply 2 * 3 4 + -2x = 6(-3 + 4x)(-8 + 4x) Multiply (-3 + 4x) * (-8 + 4x) 4 + -2x = 6(-3(-8 + 4x) + 4x * (-8 + 4x)) 4 + -2x = 6((-8 * -3 + 4x * -3) + 4x * (-8 + 4x)) 4 + -2x = 6((24 + -12x) + 4x * (-8 + 4x)) 4 + -2x = 6(24 + -12x + (-8 * 4x + 4x * 4x)) 4 + -2x = 6(24 + -12x + (-32x + 16x2)) Combine like terms: -12x + -32x = -44x 4 + -2x = 6(24 + -44x + 16x2) 4 + -2x = (24 * 6 + -44x * 6 + 16x2 * 6) 4 + -2x = (144 + -264x + 96x2) Solving 4 + -2x = 144 + -264x + 96x2 Solving for variable 'x'. Reorder the terms: 4 + -144 + -2x + 264x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2 Combine like terms: 4 + -144 = -140 -140 + -2x + 264x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2 Combine like terms: -2x + 264x = 262x -140 + 262x + -96x2 = 144 + -264x + 96x2 + -144 + 264x + -96x2 Reorder the terms: -140 + 262x + -96x2 = 144 + -144 + -264x + 264x + 96x2 + -96x2 Combine like terms: 144 + -144 = 0 -140 + 262x + -96x2 = 0 + -264x + 264x + 96x2 + -96x2 -140 + 262x + -96x2 = -264x + 264x + 96x2 + -96x2 Combine like terms: -264x + 264x = 0 -140 + 262x + -96x2 = 0 + 96x2 + -96x2 -140 + 262x + -96x2 = 96x2 + -96x2 Combine like terms: 96x2 + -96x2 = 0 -140 + 262x + -96x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + 131x + -48x2) = 0 Factor a trinomial. 2((-2 + x)(35 + -48x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(35 + -48x)' equal to zero and attempt to solve: Simplifying 35 + -48x = 0 Solving 35 + -48x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -48x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -48x = 0 + -35 -48x = 0 + -35 Combine like terms: 0 + -35 = -35 -48x = -35 Divide each side by '-48'. x = 0.7291666667 Simplifying x = 0.7291666667Solution
x = {2, 0.7291666667}
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