(2a-4)(7-3a)=(5+2a)(2a-4)

Simple and best practice solution for (2a-4)(7-3a)=(5+2a)(2a-4) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (2a-4)(7-3a)=(5+2a)(2a-4) equation:


Simplifying
(2a + -4)(7 + -3a) = (5 + 2a)(2a + -4)

Reorder the terms:
(-4 + 2a)(7 + -3a) = (5 + 2a)(2a + -4)

Multiply (-4 + 2a) * (7 + -3a)
(-4(7 + -3a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
((7 * -4 + -3a * -4) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
((-28 + 12a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
(-28 + 12a + (7 * 2a + -3a * 2a)) = (5 + 2a)(2a + -4)
(-28 + 12a + (14a + -6a2)) = (5 + 2a)(2a + -4)

Combine like terms: 12a + 14a = 26a
(-28 + 26a + -6a2) = (5 + 2a)(2a + -4)

Reorder the terms:
-28 + 26a + -6a2 = (5 + 2a)(-4 + 2a)

Multiply (5 + 2a) * (-4 + 2a)
-28 + 26a + -6a2 = (5(-4 + 2a) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = ((-4 * 5 + 2a * 5) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = ((-20 + 10a) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = (-20 + 10a + (-4 * 2a + 2a * 2a))
-28 + 26a + -6a2 = (-20 + 10a + (-8a + 4a2))

Combine like terms: 10a + -8a = 2a
-28 + 26a + -6a2 = (-20 + 2a + 4a2)

Solving
-28 + 26a + -6a2 = -20 + 2a + 4a2

Solving for variable 'a'.

Reorder the terms:
-28 + 20 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: -28 + 20 = -8
-8 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: 26a + -2a = 24a
-8 + 24a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: -6a2 + -4a2 = -10a2
-8 + 24a + -10a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Reorder the terms:
-8 + 24a + -10a2 = -20 + 20 + 2a + -2a + 4a2 + -4a2

Combine like terms: -20 + 20 = 0
-8 + 24a + -10a2 = 0 + 2a + -2a + 4a2 + -4a2
-8 + 24a + -10a2 = 2a + -2a + 4a2 + -4a2

Combine like terms: 2a + -2a = 0
-8 + 24a + -10a2 = 0 + 4a2 + -4a2
-8 + 24a + -10a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-8 + 24a + -10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 12a + -5a2) = 0

Factor a trinomial.
2((-2 + a)(2 + -5a)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + a)' equal to zero and attempt to solve: Simplifying -2 + a = 0 Solving -2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a = 0 + 2 a = 0 + 2 Combine like terms: 0 + 2 = 2 a = 2 Simplifying a = 2

Subproblem 2

Set the factor '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4

Solution

a = {2, 0.4}

See similar equations:

| d^2+10d-75=0 | | 23x+6-27x=1-7 | | lnx-2[ln(x+2)+ln(x-2)]= | | l=5w+2 | | 2h+0=-12 | | 28-14=2(x-3) | | w^2-28w-5280=0 | | 5c^2-80=0 | | 4d=-6+d | | log(x-2)+log(x-2)=1 | | 2p=-6+p | | 4x+8x-8=-172+4x+1 | | 1+2x=17-4x | | 8y+10=10y | | a^2+56=-15a | | 4x+5x+1=10 | | -4x-2x+12=3x+30 | | 6w=-7+5w | | sinx-cosy-2=0 | | 2x^2-10c-28=0 | | 3x+x+5=25 | | 2x+2+3x+3=2x+8 | | w^2-28-5280=0 | | 14x^2+7x-7=y | | 16x-5=16x^2-2 | | 3x+5i=15-20yi | | 9x^2-80y=0 | | 2(-3x+4)=26 | | 8(6x+2)=16-2x | | 3x+5i=-15-20yi | | 5y^2-80y=0 | | 2x^2+ax-a^2=0 |

Equations solver categories