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Simplifying a(a + -4)(4a + -5) = 0 Reorder the terms: a(-4 + a)(4a + -5) = 0 Reorder the terms: a(-4 + a)(-5 + 4a) = 0 Multiply (-4 + a) * (-5 + 4a) a(-4(-5 + 4a) + a(-5 + 4a)) = 0 a((-5 * -4 + 4a * -4) + a(-5 + 4a)) = 0 a((20 + -16a) + a(-5 + 4a)) = 0 a(20 + -16a + (-5 * a + 4a * a)) = 0 a(20 + -16a + (-5a + 4a2)) = 0 Combine like terms: -16a + -5a = -21a a(20 + -21a + 4a2) = 0 (20 * a + -21a * a + 4a2 * a) = 0 (20a + -21a2 + 4a3) = 0 Solving 20a + -21a2 + 4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(20 + -21a + 4a2) = 0 Factor a trinomial. a((5 + -4a)(4 + -1a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25Subproblem 3
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {0, 1.25, 4}
| https://content.thinkthroughmath.com/uploads/image/image/498968/G58L803Q1108S-9f718f361c33f798491f1bb0ce364543-6c936dbc9d573089bb5a5d4d5a6af030.png | | 6k=8w | | 6(2x-10)=36 | | 4(6n+2)+8=-152 | | 1600=13x+5y | | x+2-3x=14 | | -3a-8+6a=16 | | x+.18x=1200 | | (y+7)(y+4)=0 | | p-(-8)=14 | | 0=-6r-8r | | 4=4-3n+8n | | 3x+2y+z=50000 | | x-(-15)=0 | | =6(y+3)-2(2y+3) | | 7M^2=13M+2 | | 34.2=9(x+1.2) | | P(4)p=0.40 | | 7.21+x=9.82 | | -1=p/-3 | | 7m^2=1M+2 | | Y-4=-3(x-5) | | 9.04=(0.55+2x)(0.3+2x) | | 7x-45=5 | | 2p^2+15p+18=0 | | -1=p/9-4 | | 8x-8=4x+2(2x-4) | | 2x^2+18x-144=0 | | v=u+(at) | | Y+2x=12z | | 6+0.25x=21 | | 3e^2x=648 |
