-4(a-7)=a(a-1)

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Solution for -4(a-7)=a(a-1) equation:


Simplifying
-4(a + -7) = a(a + -1)

Reorder the terms:
-4(-7 + a) = a(a + -1)
(-7 * -4 + a * -4) = a(a + -1)
(28 + -4a) = a(a + -1)

Reorder the terms:
28 + -4a = a(-1 + a)
28 + -4a = (-1 * a + a * a)
28 + -4a = (-1a + a2)

Solving
28 + -4a = -1a + a2

Solving for variable 'a'.

Combine like terms: -4a + a = -3a
28 + -3a + -1a2 = -1a + a2 + a + -1a2

Reorder the terms:
28 + -3a + -1a2 = -1a + a + a2 + -1a2

Combine like terms: -1a + a = 0
28 + -3a + -1a2 = 0 + a2 + -1a2
28 + -3a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
28 + -3a + -1a2 = 0

Factor a trinomial.
(4 + -1a)(7 + a) = 0

Subproblem 1

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 = 4

Subproblem 2

Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7

Solution

a = {4, -7}

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